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Consistent Estimates (consistent + estimate)

Distribution by Scientific Domains

Mathematics and Statistics	47%
Medical Sciences	19%
Business, Economics, Finance and Accounting	14%
Earth and Environmental Science	9%
2 Other Domains	11%

Selected Abstracts

Comparing alternative models: log vs Cox proportional hazard?

HEALTH ECONOMICS, Issue 8 2004
Anirban Basu
Abstract Health economists often use log models (based on OLS or generalized linear models) to deal with skewed outcomes such as those found in health expenditures and inpatient length of stay. Some recent studies have employed Cox proportional hazard regression as a less parametric alternative to OLS and GLM models, even when there was no need to correct for censoring. This study examines how well the alternative estimators behave econometrically in terms of bias when the data are skewed to the right. Specifically we provide evidence on the performance of the Cox model under a variety of data generating mechanisms and compare it to the estimators studied recently in Manning and Mullahy (2001). No single alternative is best under all of the conditions examined here. However, the gamma regression model with a log link seems to be more robust to alternative data generating mechanisms than either OLS on ln(y) or Cox proportional hazards regression. We find that the proportional hazard assumption is an essential requirement to obtain consistent estimate of the E(y,x) using the Cox model. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Measuring income related inequality in health: standardisation and the partial concentration index

HEALTH ECONOMICS, Issue 10 2003
Hugh Gravelle
Abstract The partial concentration index (PCI) is commonly used as a measure of income related inequality in health after removing the effects of standardising variables such as age and gender which affect health, are correlated with income, but not amenable to policy. Both direct and indirect standardisation have been used to remove the effects of standardising variables. The paper shows that with individual level data direct standardisation is possible using the coefficients from a linear regression of health on income and the standardising variables and yields a consistent estimate of the PCI. Indirect standardisation estimates the effects of the standardising variables on health from a health regression which excludes income. The coefficients on the standardising variables include some of the effects of income on health if income is correlated with the standardising variables. Using these coefficients to remove the effects of the standardising variables also removes some of the effect of income on health and leads to an inconsistent estimate of the PCI. Indirect standardisation underestimates the PCI irrespective of the signs of the correlations of standardising variables and income with each other and with health. An adaptation of the PCI when the marginal effect of income on health depends on the standardising variables is also proposed. Copyright © 2003 John Wiley & Sons, Ltd. [source]

On the non-negative garrotte estimator

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2007
Ming Yuan
Summary., We study the non-negative garrotte estimator from three different aspects: consistency, computation and flexibility. We argue that the non-negative garrotte is a general procedure that can be used in combination with estimators other than the original least squares estimator as in its original form. In particular, we consider using the lasso, the elastic net and ridge regression along with ordinary least squares as the initial estimate in the non-negative garrotte. We prove that the non-negative garrotte has the nice property that, with probability tending to 1, the solution path contains an estimate that correctly identifies the set of important variables and is consistent for the coefficients of the important variables, whereas such a property may not be valid for the initial estimators. In general, we show that the non-negative garrotte can turn a consistent estimate into an estimate that is not only consistent in terms of estimation but also in terms of variable selection. We also show that the non-negative garrotte has a piecewise linear solution path. Using this fact, we propose an efficient algorithm for computing the whole solution path for the non-negative garrotte. Simulations and a real example demonstrate that the non-negative garrotte is very effective in improving on the initial estimator in terms of variable selection and estimation accuracy. [source]

Bootstrapping a weighted linear estimator of the ARCH parameters

JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2009
Arup Bose
Abstract., A standard assumption while deriving the asymptotic distribution of the quasi maximum likelihood estimator in ARCH models is that all ARCH parameters must be strictly positive. This assumption is also crucial in deriving the limit distribution of appropriate linear estimators (LE). We propose a weighted linear estimator (WLE) of the ARCH parameters in the classical ARCH model and show that its limit distribution is multivariate normal even when some of the ARCH coefficients are zero. The asymptotic dispersion matrix involves unknown quantities. We consider appropriate bootstrapped version of this WLE and prove that it is asymptotically valid in the sense that the bootstrapped distribution (given the data) is a consistent estimate (in probability) of the distribution of the WLE. Although we do not show theoretically that the bootstrap outperforms the normal approximation, our simulations demonstrate that it yields better approximations than the limiting normal. [source]

A note on estimation by least squares for harmonic component models

JOURNAL OF TIME SERIES ANALYSIS, Issue 5 2003
A. M. Walker
Abstract. Let observations (X1,,,Xn) be generated by a harmonic model such that Xt=A0 cos ,0t+B0 sin ,0t+,t, where A0,B0,,0 are constants and (,t) is a stationary process with zero mean and finite variance. The estimation of A0,B0,,0 by the method of least squares is considered. It is shown that, without any restriction on , in the minimization procedure, the estimate is an n -consistent estimate of ,0, and hence () has the usual asymptotic distribution. The extension to a harmonic model with k>1 components is discussed. The case k=2 is considered in detail, but it was only found possible to establish the result under the restriction that both angular frequencies lie in the interval [source]

Areal PMP distribution of one-day to three-day duration over India

METEOROLOGICAL APPLICATIONS, Issue 4 2002
C P R Clark Rakhecha
There is a need to assess the areal depth of the probable maximum precipitation (PMP) over specified catchment areas for the safe construction of dam spillways. The large number of dams in India, coupled with their risk of failure, makes this need imperative both for the maximum use of water resources and for public safety. On the basis of rainfall data for the heaviest storms that occurred in different parts of India during the period 1880,1983, improved estimates of one-, two-, and three-day point PMP for India have been made. In this paper the distribution of areal PMP over specified catchment sizes is provided for the first time. The areal reduction factors (ARF) were based on envelope curves of major storms to give the ARF for areas of 10,20,000 km2 . These factors were found to vary from 1.0 to 0.41, though there was no real difference between durations of rainfall. These values of ARF were then multiplied by values of one- to three-day PMP. The resulting maps allow a broad description of the spatial distribution of areal PMP and also provide a rapid and consistent estimate of the probable maximum flood (PMF) from the PMP. For 500 km2 the areal PMP varies from 40 to 120 cm for one-day duration; from 70 to 200 cm for twoday duration; and from 75 to 270 cm for three-day duration. The pattern of PMP is consistent with the geography and available moisture. Copyright © 2002 Royal Meteorological Society. [source]

Two measures of the shape of the dark halo of the Milky Way

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2000
Rob P. Olling
In order to test the reliability of determinations of the shapes of dark-matter haloes of the galaxies, we have made such measurements for the Milky Way by two independent methods. First, we have combined the measurements of the overall mass distribution of the Milky Way derived from its rotation curve and the measurements of the amount of dark matter in the solar neighbourhood obtained from stellar kinematics to determine the flattening of the dark halo. Secondly, we have used the established technique based on the variation in thickness of the Milky Way's H i layer with radius: by assuming that the H i gas is in hydrostatic equilibrium in the gravitational potential of a galaxy, one can use the observed flaring of the gas layer to determine the shape of the dark halo. These techniques are found to produce a consistent estimate for the flattening of the dark-matter halo, with a shortest-to-longest axis ratio of q,0.8, but only if one adopts somewhat non-standard values for the distance to the Galactic centre, R0, and the local Galactic rotation speed, ,0. For consistency, one requires values of R0,7.6 kpc and ,0,190 km s,1. The results depend on the Galactic constants because the adopted values affect both distance measurements within the Milky Way and the shape of the rotation curve, which, in turn, alter the inferred halo shape. Although differing significantly from the current IAU-sanctioned values, these upper limits are consistent with all existing observational constraints. If future measurements confirm these lower values for the Galactic constants, then the validity of the gas-layer-flaring method will be confirmed. Further, dark-matter candidates such as cold molecular gas and massive decaying neutrinos, which predict very flat dark haloes with q,0.2, will be ruled out. Conversely, if the Galactic constants were found to be close to the more conventional values, then there would have to be some systematic error in the methods for measuring dark halo shapes, so the existing modelling techniques would have to be viewed with some scepticism. [source]

Modified weights based generalized quasilikelihood inferences in incomplete longitudinal binary models

THE CANADIAN JOURNAL OF STATISTICS, Issue 2 2010
Brajendra C. Sutradhar
Abstract In an incomplete longitudinal set up, a small number of repeated responses subject to an appropriate missing mechanism along with a set of covariates are collected from a large number of independent individuals over a small period of time. In this set up, the regression effects of the covariates are routinely estimated by solving certain inverse weights based generalized estimating equations. These inverse weights are introduced to make the estimating equation unbiased so that a consistent estimate of the regression parameter vector may be obtained. In the existing studies, these weights are in general formulated conditional on the past responses. Since the past responses follow a correlation structure, the present study reveals that if the longitudinal data subject to missing mechanism are generated by accommodating the longitudinal correlation structure, the conditional weights based on past correlated responses may yield biased and hence inconsistent regression estimates. The bias appears to get larger as the correlation increases. As a remedy, in this paper the authors proposed a modification to the formulation of the existing weights so that weights are not affected directly or indirectly by the correlations. They have then exploited these modified weights to form a weighted generalized quasi-likelihood estimating equation that yields unbiased and hence consistent estimates for the regression effects irrespective of the magnitude of correlation. The efficiencies of the regression estimates follow due to the use of the true correlation structure as a separate longitudinal weights matrix in the estimating equation. The Canadian Journal of Statistics © 2010 Statistical Society of Canada Dans un cadre de données longitudinales incomplètes, nous observons un petit nombre de réponses répétées sujettes à un mécanisme de valeurs manquantes approprié avec un ensemble de covariables provenant d'un grand nombre d'individus indépendants observés sur une petite période de temps. Dans ce cadre, les composantes de régression des covariables sont habituellement estimées en résolvant certains poids inverses obtenus à partir d'équations d'estimation généralisées. Ces poids inverses sont utilisés afin de rendre les équations d'estimation sans biais et ainsi permettre d'obtenir des estimateurs cohérents pour le vecteur des paramètres de régressions. Dans les études déjà existantes, ces poids sont généralement formulés conditionnement aux réponses passées. Puisque les réponses passées possèdent une structure de corrélation, cet article révèle que si les données longitudinales, soumises à un mécanisme de valeurs manquantes, sont générées en adaptant la structure de corrélation longitudinale, alors les poids conditionnels basés sur les réponses corrélées passées peuvent mener à des estimations biaisées, et conséquemment non cohérentes, des composantes de régression. Ce biais semble augmenter lorsque la corrélation augmente. Pour remédier à cette situation, les auteurs proposent dans cet article, une modification aux poids déjà existants afin que ceux-ci ne soient plus affectés directement ou indirectement par les corrélations. Par la suite, ils ont exploité ces poids modifiés pour obtenir une équation d'estimation généralisée pondérée basée sur la quasi-vraisemblance qui conduit à des estimateurs sans biais, et ainsi cohérents, pour les composantes de régression sans égard à l'ampleur de la corrélation. L'efficacité de ces estimateurs est attribuable à l'utilisation de la vraie structure de corrélation comme matrice de poids longitudinale à part dans l'équation d'estimation. La revue canadienne de statistique © 2010 Société statistique du Canada [source]

Estimating the order of a hidden markov model

THE CANADIAN JOURNAL OF STATISTICS, Issue 4 2002
Rachel J. Mackay
Abstract While the estimation of the parameters of a hidden Markov model has been studied extensively, the consistent estimation of the number of hidden states is still an unsolved problem. The AIC and BIC methods are used most commonly, but their use in this context has not been justified theoretically. The author shows that for many common models, the penalized minimum-distance method yields a consistent estimate of the number of hidden states in a stationary hidden Markov model. In addition to addressing the identifiability issues, she applies her method to a multiple sclerosis data set and assesses its performance via simulation. Bien que les travaux traitant de I'estimation des paramétres d'une chatne de Markov cachéd soient nombreux, le probléme d'estimer de facon convergente le nombre détats cachés reste ouvert. Les méthodes du CIA et du CIB sont souvent utilisées a cette fin, sans toutefois que leur emploi ait été justifié théoriquement. L'auteur montre ici que, sous des conditions convenables, la méthode de distance minimum pénalisée conduit à une estimation convergente du nombre d'états cachés dans une chaine de Markov cachée stationnaire. En plus d'aborder le probléme d'identifiabilité, elle applique sa méthode à des données concernant la sclérose en plaques et en évalue la performance a taille finie par voie de simulation. [source]

Partly Functional Temporal Process Regression with Semiparametric Profile Estimating Functions

BIOMETRICS, Issue 2 2009
Jun Yan
Summary Marginal mean models of temporal processes in event time data analysis are gaining more attention for their milder assumptions than the traditional intensity models. Recent work on fully functional temporal process regression (TPR) offers great flexibility by allowing all the regression coefficients to be nonparametrically time varying. The existing estimation procedure, however, prevents successive goodness-of-fit test for covariate coefficients in comparing a sequence of nested models. This article proposes a partly functional TPR model in the line of marginal mean models. Some covariate effects are time independent while others are completely unspecified in time. This class of models is very rich, including the fully functional model and the semiparametric model as special cases. To estimate the parameters, we propose semiparametric profile estimating equations, which are solved via an iterative algorithm, starting at a consistent estimate from a fully functional model in the existing work. No smoothing is needed, in contrast to other varying-coefficient methods. The weak convergence of the resultant estimators are developed using the empirical process theory. Successive tests of time-varying effects and backward model selection procedure can then be carried out. The practical usefulness of the methodology is demonstrated through a simulation study and a real example of recurrent exacerbation among cystic fibrosis patients. [source]

Bounds on Parameters in Panel Dynamic Discrete Choice Models

ECONOMETRICA, Issue 3 2006
Bo E. Honoré
Identification of dynamic nonlinear panel data models is an important and delicate problem in econometrics. In this paper we provide insights that shed light on the identification of parameters of some commonly used models. Using these insights, we are able to show through simple calculations that point identification often fails in these models. On the other hand, these calculations also suggest that the model restricts the parameter to lie in a region that is very small in many cases, and the failure of point identification may, therefore, be of little practical importance in those cases. Although the emphasis is on identification, our techniques are constructive in that they can easily form the basis for consistent estimates of the identified sets. [source]

A Parametric Approach to Flexible Nonlinear Inference

ECONOMETRICA, Issue 3 2001
James D. Hamilton
This paper proposes a new framework for determining whether a given relationship is nonlinear, what the nonlinearity looks like, and whether it is adequately described by a particular parametric model. The paper studies a regression or forecasting model of the form yt=,(xt)+,t where the functional form of ,(,) is unknown. We propose viewing ,(,) itself as the outcome of a random process. The paper introduces a new stationary random field m(,) that generalizes finite-differenced Brownian motion to a vector field and whose realizations could represent a broad class of possible forms for ,(,). We view the parameters that characterize the relation between a given realization of m(,) and the particular value of ,(,) for a given sample as population parameters to be estimated by maximum likelihood or Bayesian methods. We show that the resulting inference about the functional relation also yields consistent estimates for a broad class of deterministic functions ,(,). The paper further develops a new test of the null hypothesis of linearity based on the Lagrange multiplier principle and small-sample confidence intervals based on numerical Bayesian methods. An empirical application suggests that properly accounting for the nonlinearity of the inflation-unemployment trade-off may explain the previously reported uneven empirical success of the Phillips Curve. [source]

Modelling Probabilities of Devaluations

ECONOMICA, Issue 281 2004
Gabriela Mundaca
I show why, when the realized rates of depreciation within the exchange rate band are regressed on a given information set and conditioned on (ex post) actual no realignment (à la drift adjustment), a ,peso problem' is still encountered. The reason is that the frequency of realignments in the data need not be the same as the frequency of the (even small) subjective probabilities that a realignment may take place. I suggest an alternative approach to solve the peso problem and provide consistent estimates. My estimates of the expected realignment rates are greater than the ones obtained using the drift adjustment method. [source]

On parameter estimation for excitation control of synchronous generators

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 5 2004
Martha Galaz
Abstract This paper deals with the problem of identification of the network parameters and the desired equilibrium in applications of excitation control for synchronous generators. Our main contribution is the construction of a new non-linear identifier that provides asymptotically consistent estimates (with guaranteed transient bounds) of the line impedance and the equilibrium for the classical three-dimensional flux-decay model of a single generator connected to an infinite bus. This model is non-linear, and non-linearly parameterized, and the equilibria depend also non-linearly on the unknown parameters. The proposed estimator can be used, adopting a certainty equivalent approach, to make adaptive any power system stabilizer that relies on the knowledge of these parameters. The behaviour of the scheme is illustrated in two simulated case studies with the interconnection and damping assignment passivity-based controller recently proposed by the authors. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Doppler ultrasound assessment of posterior tibial artery size in humans

JOURNAL OF CLINICAL ULTRASOUND, Issue 5 2006
Manning J. Sabatier PhD
Abstract Purpose. The difference between structural remodeling and changes in tone of peripheral arteries in the lower extremities has not been evaluated. The purpose of this study was to (1) evaluate the day-to-day reproducibility and interobserver reliability (IOR) of posterior tibial artery (PTA) diameter measurements and (2) evaluate the effect of posture on PTA diameter at rest (Drest), during 10 minutes of proximal cuff occlusion (Dmin), and after the release of cuff occlusion (Dmax), as well as range (Dmax , Dmin) and constriction [(Dmax , Drest)/(Dmax , Dmin) × 100] in vivo. Methods. We used B-mode sonography to image the PTA during each condition. Results. Day-to-day reliability was good for Drest (intraclass correlation coefficient [ICC] 0.95; mean difference 4.2%), Dmin (ICC 0.93; mean difference 5.4%), and Dmax (ICC 0.99; mean difference 2.2%). The coefficient of repeatability for IOR was 70.5 ,m, with a mean interobserver error of 4.7 ,m. The seated position decreased Drest (2.6 ± 0.2 to 2.4 ± 0.3 mm; p = 0.002), increased Dmin (2.1 ± 0.2 to 2.4 ± 0.2 mm; p = 0.001), and decreased Dmax (3.1 ± 0.4 to 2.8 ± 0.3 mm; p < 0.001) compared with the supine position. The seated position also decreased arterial range (Dmax , Dmin) from 0.9 ± 0.2 to 0.5 ± 0.1 mm (p = 0.003) and increased basal arterial constriction from 57 ± 19% to 105 ± 27% (p = 0.007). Conclusions. The system employed for measuring PTA diameter yields unbiased and consistent estimates. Furthermore, lower extremity arterial constriction and range change with posture in a manner consistent with known changes in autonomic activity. © 2006 Wiley Periodicals, Inc. J Clin Ultrasound 34:223,230, 2006 [source]

Joint generalized estimating equations for multivariate longitudinal binary outcomes with missing data: an application to acquired immune deficiency syndrome data

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES A (STATISTICS IN SOCIETY), Issue 1 2009
Stuart R. Lipsitz
Summary., In a large, prospective longitudinal study designed to monitor cardiac abnormalities in children born to women who are infected with the human immunodeficiency virus, instead of a single outcome variable, there are multiple binary outcomes (e.g. abnormal heart rate, abnormal blood pressure and abnormal heart wall thickness) considered as joint measures of heart function over time. In the presence of missing responses at some time points, longitudinal marginal models for these multiple outcomes can be estimated by using generalized estimating equations (GEEs), and consistent estimates can be obtained under the assumption of a missingness completely at random mechanism. When the missing data mechanism is missingness at random, i.e. the probability of missing a particular outcome at a time point depends on observed values of that outcome and the remaining outcomes at other time points, we propose joint estimation of the marginal models by using a single modified GEE based on an EM-type algorithm. The method proposed is motivated by the longitudinal study of cardiac abnormalities in children who were born to women infected with the human immunodeficiency virus, and analyses of these data are presented to illustrate the application of the method. Further, in an asymptotic study of bias, we show that, under a missingness at random mechanism in which missingness depends on all observed outcome variables, our joint estimation via the modified GEE produces almost unbiased estimates, provided that the correlation model has been correctly specified, whereas estimates from standard GEEs can lead to substantial bias. [source]

Modified weights based generalized quasilikelihood inferences in incomplete longitudinal binary models

A review on the use of the adjoint method in four-dimensional atmospheric-chemistry data assimilation

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 576 2001
K.-Y. Wang
Abstract In this paper we review a theoretical formulation of the adjoint method to be used in four-dimensional (4D) chemistry data assimilation. The goal of the chemistry data assimilation is to combine an atmospheric-chemistry model and actual observations to produce the best estimate of the chemistry of the atmosphere. The observational dataset collected during the past decades is an unprecedented expansion of our knowledge of the atmosphere. The exploitation of these data is the best way to advance our understanding of atmospheric chemistry, and to develop chemistry models for chemistry-climate prediction. The assimilation focuses on estimating the state of the chemistry in a chemically and dynamically consistent manner (if the model allows online interactions between chemistry and dynamics). In so doing, we can: produce simultaneous and chemically consistent estimates of all species (including model parameters), observed and unobserved; fill in data voids; test the photochemical theories used in the chemistry models. In this paper, the Hilbert space is first formulated from the geometric structure of the Banach space, followed by the development of the adjoint operator in Hilbert space. The principle of the adjoint method is described, followed by two examples which show the relationship of the gradient of the cost function with respect to the output vector and the gradient of the cost function with respect to the input vector. Applications to chemistry data assimilation are presented for both continuous and discrete cases. The 4D data variational adjoint method is then tested in the assimilation of stratospheric chemistry using a simple catalytic ozone-destruction mechanism, and the test results indicate that the performance of the assimilation method is good. [source]

ESTIMATING COMPONENTS IN FINITE MIXTURES AND HIDDEN MARKOV MODELS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2005
D.S. Poskitt
Summary When the unobservable Markov chain in a hidden Markov model is stationary the marginal distribution of the observations is a finite mixture with the number of terms equal to the number of the states of the Markov chain. This suggests the number of states of the unobservable Markov chain can be estimated by determining the number of mixture components in the marginal distribution. This paper presents new methods for estimating the number of states in a hidden Markov model, and coincidentally the unknown number of components in a finite mixture, based on penalized quasi-likelihood and generalized quasi-likelihood ratio methods constructed from the marginal distribution. The procedures advocated are simple to calculate, and results obtained in empirical applications indicate that they are as effective as current available methods based on the full likelihood. Under fairly general regularity conditions, the methods proposed generate strongly consistent estimates of the unknown number of states or components. [source]

The burden of coronary heart disease in M,ori: population-based estimates for 2000-02

AUSTRALIAN AND NEW ZEALAND JOURNAL OF PUBLIC HEALTH, Issue 4 2009
Martin Tobias
Abstract Objective: To estimate coronary heart disease (CHD) incidence, prevalence, survival, case fatality and mortality for M,ori, in order to support service planning and resource allocation. Methods: Incidence was defined as first occurrence of a major coronary event, i.e. the sum of first CHD hospital admissions and out-of-hospital CHD deaths in people without a hospital admission for CHD in the preceding five years. Data for the years 2000-02 were sourced from the New Zealand Health Information Service and record linkage was carried out using a unique national identifier, the national health index. Results: Compared to the non-M,ori population, M,ori had both elevated CHD incidence and higher case fatality. Median age at onset of CHD was younger for M,ori, reflecting both higher age specific risks and younger population age structure. The lifetable risk of CHD for M,ori was estimated at 37% (males) and 34% (females), only moderately higher than the corresponding estimates for the non-M,ori population, despite higher M,ori CHD incidence. This reflects the offsetting effect of the higher ,other cause' mortality experienced by M,ori. Median duration of survival with CHD was similar to that of the non-M,ori population for M,ori males but longer for M,ori females, which is most likely related to the earlier age of onset. Conclusions: This study has generated consistent estimates of CHD incidence, prevalence, survival, case fatality and mortality for M,ori in 2000-02. The inequality identified in CHD incidence calls for a renewed effort in primary prevention. The inequality in CHD case fatality calls for improvement in access for M,ori to secondary care services. [source]

A Flexible Approach to Measurement Error Correction in Case,Control Studies

BIOMETRICS, Issue 4 2008
A. Guolo
Summary We investigate the use of prospective likelihood methods to analyze retrospective case,control data where some of the covariates are measured with error. We show that prospective methods can be applied and the case,control sampling scheme can be ignored if one adequately models the distribution of the error-prone covariates in the case,control sampling scheme. Indeed, subject to this, the prospective likelihood methods result in consistent estimates and information standard errors are asymptotically correct. However, the distribution of such covariates is not the same in the population and under case,control sampling, dictating the need to model the distribution flexibly. In this article, we illustrate the general principle by modeling the distribution of the continuous error-prone covariates using the skewnormal distribution. The performance of the method is evaluated through simulation studies, which show satisfactory results in terms of bias and coverage. Finally, the method is applied to the analysis of two data sets which refer, respectively, to a cholesterol study and a study on breast cancer. [source]