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Consistent Estimator (consistent + estimator)
Selected AbstractsEstimation of Nonlinear Models with Measurement ErrorECONOMETRICA, Issue 1 2004Susanne M. Schennach This paper presents a solution to an important econometric problem, namely the root n consistent estimation of nonlinear models with measurement errors in the explanatory variables, when one repeated observation of each mismeasured regressor is available. While a root n consistent estimator has been derived for polynomial specifications (see Hausman, Ichimura, Newey, and Powell (1991)), such an estimator for general nonlinear specifications has so far not been available. Using the additional information provided by the repeated observation, the suggested estimator separates the measurement error from the "true" value of the regressors thanks to a useful property of the Fourier transform: The Fourier transform converts the integral equations that relate the distribution of the unobserved "true" variables to the observed variables measured with error into algebraic equations. The solution to these equations yields enough information to identify arbitrary moments of the "true," unobserved variables. The value of these moments can then be used to construct any estimator that can be written in terms of moments, including traditional linear and nonlinear least squares estimators, or general extremum estimators. The proposed estimator is shown to admit a representation in terms of an influence function, thus establishing its root n consistency and asymptotic normality. Monte Carlo evidence and an application to Engel curve estimation illustrate the usefulness of this new approach. [source] Linkage analysis with sequential imputationGENETIC EPIDEMIOLOGY, Issue 1 2003Zachary Skrivanek Abstract Multilocus calculations, using all available information on all pedigree members, are important for linkage analysis. Exact calculation methods in linkage analysis are limited in either the number of loci or the number of pedigree members they can handle. In this article, we propose a Monte Carlo method for linkage analysis based on sequential imputation. Unlike exact methods, sequential imputation can handle large pedigrees with a moderate number of loci in its current implementation. This Monte Carlo method is an application of importance sampling, in which we sequentially impute ordered genotypes locus by locus, and then impute inheritance vectors conditioned on these genotypes. The resulting inheritance vectors, together with the importance sampling weights, are used to derive a consistent estimator of any linkage statistic of interest. The linkage statistic can be parametric or nonparametric; we focus on nonparametric linkage statistics. We demonstrate that accurate estimates can be achieved within a reasonable computing time. A simulation study illustrates the potential gain in power using our method for multilocus linkage analysis with large pedigrees. We simulated data at six markers under three models. We analyzed them using both sequential imputation and GENEHUNTER. GENEHUNTER had to drop between 38,54% of pedigree members, whereas our method was able to use all pedigree members. The power gains of using all pedigree members were substantial under 2 of the 3 models. We implemented sequential imputation for multilocus linkage analysis in a user-friendly software package called SIMPLE. Genet Epidemiol 25:25,35, 2003. © 2003 Wiley-Liss, Inc. [source] Asymmetric power distribution: Theory and applications to risk measurementJOURNAL OF APPLIED ECONOMETRICS, Issue 5 2007Ivana Komunjer Theoretical literature in finance has shown that the risk of financial time series can be well quantified by their expected shortfall, also known as the tail value-at-risk. In this paper, I construct a parametric estimator for the expected shortfall based on a flexible family of densities, called the asymmetric power distribution (APD). The APD family extends the generalized power distribution to cases where the data exhibits asymmetry. The first contribution of the paper is to provide a detailed description of the properties of an APD random variable, such as its quantiles and expected shortfall. The second contribution of the paper is to derive the asymptotic distribution of the APD maximum likelihood estimator (MLE) and construct a consistent estimator for its asymptotic covariance matrix. The latter is based on the APD score whose analytic expression is also provided. A small Monte Carlo experiment examines the small sample properties of the MLE and the empirical coverage of its confidence intervals. An empirical application to four daily financial market series reveals that returns tend to be asymmetric, with innovations which cannot be modeled by either Laplace (double-exponential) or Gaussian distribution, even if we allow the latter to be asymmetric. In an out-of-sample exercise, I compare the performances of the expected shortfall forecasts based on the APD-GARCH, Skew- t -GARCH and GPD-EGARCH models. While the GPD-EGARCH 1% expected shortfall forecasts seem to outperform the competitors, all three models perform equally well at forecasting the 5% and 10% expected shortfall. Copyright © 2007 John Wiley & Sons, Ltd. [source] First-Order Autoregressive Processes with Heterogeneous PersistenceJOURNAL OF TIME SERIES ANALYSIS, Issue 3 2003JOANN JASIAK Abstract. We propose a semi-nonparametric method of identification and estimation for Gaussian autoregressive processes with stochastic autoregressive coefficients. The autoregressive coefficient is considered as a latent process with either a moving average or regime switching representation. We develop a consistent estimator of the distribution of the autoregressive coefficient based on nonlinear canonical decomposition of the observed process. The approach is illustrated by simulations. [source] Corrected local polynomial estimation in varying-coefficient models with measurement errorsTHE CANADIAN JOURNAL OF STATISTICS, Issue 3 2006Jinhong You Abstract The authors study a varying-coefficient regression model in which some of the covariates are measured with additive errors. They find that the usual local linear estimator (LLE) of the coefficient functions is biased and that the usual correction for attenuation fails to work. They propose a corrected LLE and show that it is consistent and asymptotically normal, and they also construct a consistent estimator for the model error variance. They then extend the generalized likelihood technique to develop a goodness of fit test for the model. They evaluate these various procedures through simulation studies and use them to analyze data from the Framingham Heart Study. Estimation polynomiale locale corrigée dans les modèles à coefficients variables comportant des erreurs de mesure Les auteurs s'intéressent à un modèle de régression à coefficients variables dont certaines cova-riables sont entachées d'erreurs additives. Ils montrent que l'estimateur localement linéaire (ELL) usuel des coefficients fonctionnels est biaisé et que le facteur de correction habituel du phénomène d'atténuation est inefficace. Ils proposent une version corrigée de l'ELL qui s'avère convergente et asymptotiquement normale; ils suggèrent aussi une estimation convergente de la variance du terme d'erreur du modèle. Une adaptation de la technique de vraisemblance généralisée leur permet en outre d'élaborer un test d'adéquation du modèle. Ils évaluent ces diverses procédures par voie de simulation et s'en servent pour analyser des données issues de l'étude Framingham sur les risques cardiométaboliques. [source] Nonparametric two-step regression estimation when regressors and error are dependentTHE CANADIAN JOURNAL OF STATISTICS, Issue 2 2000Jons Pinkse Abstract This paper considers estimation of the function g in the model Yt = g(Xt ) + ,t when E(,t|Xt) , 0 with nonzero probability. We assume the existence of an instrumental variable Zt that is independent of ,t, and of an innovation ,t = Xt , E(Xt|Zt). We use a nonparametric regression of Xt on Zt to obtain residuals ,t, which in turn are used to obtain a consistent estimator of g. The estimator was first analyzed by Newey, Powell & Vella (1999) under the assumption that the observations are independent and identically distributed. Here we derive a sample mean-squared-error convergence result for independent identically distributed observations as well as a uniform-convergence result under time-series dependence. Cet article concerne l'estimation de la fonction g dans le modèle Yt = g(Xt) + ,t où E(,t| Xt) , 0 avec probabilité non nulle. Les auteurs supposent l'existence d'une 'variable instrumentale' Zt qui est indépendante de ,t et de l'innovation ,t = Xt , E(Xt|Zt). Les résidus ,t déduits d'une régression non paramétrique de Xt sur Zt permettent d'obtenir une estimation convergente de g. Cette façon de procéder avait déjà été proposée par Newey, Powell & Vella (1999) dans le cas où les observations for-ment un échantillon aléatoire. Les auteurs démontrent ici la convergence de 1'erreur quadratique moyenne expérimentale sous les m,mes conditions et établissent un résultat de convergence uniforme sous des conditions de dépendance sérielle entre les observations. [source] Is It Inefficient Investment that Causes the Diversification Discount?THE JOURNAL OF FINANCE, Issue 5 2001Toni M. Whited Diversified conglomerates are valued less than matched portfolios of pure-play firms. Recent studies find that this diversification discount results from conglomerates' inefficient allocation of capital expenditures across divisions. Much of this work uses Tobin's q as a proxy for investment opportunities, therefore hypothesizing that q is a good proxy. This paper treats measurement error in q. Using a measurement-error consistent estimator on the sorts regressions in the literature, I find no evidence of inefficient allocation of investment. The results in the literature appear to be artifacts of measurement error and of the correlation between investment opportunities and liquidity. [source] A New Nonparametric Approach for Baseline Covariate Adjustment for Two-Group Comparative StudiesBIOMETRICS, Issue 4 2008Alexander Schacht Summary We consider two-armed clinical trials in which the response and/or the covariates are observed on either a binary, ordinal, or continuous scale. A new general nonparametric (NP) approach for covariate adjustment is presented using the notion of a relative effect to describe treatment effects. The relative effect is defined by the probability of observing a higher response in the experimental than in the control arm. The notion is invariant under monotone transformations of the data and is therefore especially suitable for ordinal data. For a normal or binary distributed response the relative effect is the transformed effect size or the difference of response probability, respectively. An unbiased and consistent NP estimator for the relative effect is presented. Further, we suggest a NP procedure for correcting the relative effect for covariate imbalance and random covariate imbalance, yielding a consistent estimator for the adjusted relative effect. Asymptotic theory has been developed to derive test statistics and confidence intervals. The test statistic is based on the joint behavior of the estimated relative effect for the response and the covariates. It is shown that the test statistic can be used to evaluate the treatment effect in the presence of (random) covariate imbalance. Approximations for small sample sizes are considered as well. The sampling behavior of the estimator of the adjusted relative effect is examined. We also compare the probability of a type I error and the power of our approach to standard covariate adjustment methods by means of a simulation study. Finally, our approach is illustrated on three studies involving ordinal responses and covariates. [source] Cox Regression Methods for Two-Stage Randomization DesignsBIOMETRICS, Issue 2 2007Yuliya Lokhnygina Summary Two-stage randomization designs (TSRD) are becoming increasingly common in oncology and AIDS clinical trials as they make more efficient use of study participants to examine therapeutic regimens. In these designs patients are initially randomized to an induction treatment, followed by randomization to a maintenance treatment conditional on their induction response and consent to further study treatment. Broader acceptance of TSRDs in drug development may hinge on the ability to make appropriate intent-to-treat type inference within this design framework as to whether an experimental induction regimen is better than a standard induction regimen when maintenance treatment is fixed. Recently Lunceford, Davidian, and Tsiatis (2002, Biometrics58, 48,57) introduced an inverse probability weighting based analytical framework for estimating survival distributions and mean restricted survival times, as well as for comparing treatment policies at landmarks in the TSRD setting. In practice Cox regression is widely used and in this article we extend the analytical framework of Lunceford et al. (2002) to derive a consistent estimator for the log hazard in the Cox model and a robust score test to compare treatment policies. Large sample properties of these methods are derived, illustrated via a simulation study, and applied to a TSRD clinical trial. [source] Legendre polynomial kernel estimation of a density function with censored observations and an application to clinical trialsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2007Simeon M. Berman Let f(x), x , ,M, M , 1, be a density function on ,M, and X1, ,., Xn a sample of independent random vectors with this common density. For a rectangle B in ,M, suppose that the X's are censored outside B, that is, the value Xk is observed only if Xk , B. The restriction of f(x) to x , B is clearly estimable by established methods on the basis of the censored observations. The purpose of this paper is to show how to extrapolate a particular estimator, based on the censored sample, from the rectangle B to a specified rectangle C containing B. The results are stated explicitly for M = 1, 2, and are directly extendible to M , 3. For M = 2, the extrapolation from the rectangle B to the rectangle C is extended to the case where B and C are triangles. This is done by means of an elementary mapping of the positive quarter-plane onto the strip {(u, v): 0 , u , 1, v > 0}. This particular extrapolation is applied to the estimation of the survival distribution based on censored observations in clinical trials. It represents a generalization of a method proposed in 2001 by the author [2]. The extrapolator has the following form: For m , 1 and n , 1, let Km, n(x) be the classical kernel estimator of f(x), x , B, based on the orthonormal Legendre polynomial kernel of degree m and a sample of n observed vectors censored outside B. The main result, stated in the cases M = 1, 2, is an explicit bound for E|Km, n(x) , f(x)| for x , C, which represents the expected absolute error of extrapolation to C. It is shown that the extrapolator is a consistent estimator of f(x), x , C, if f is sufficiently smooth and if m and n both tend to , in a way that n increases sufficiently rapidly relative to m. © 2006 Wiley Periodicals, Inc. [source] Food expenditure patterns of the Hispanic population in the United StatesAGRIBUSINESS : AN INTERNATIONAL JOURNAL, Issue 2 2002Bruno A. Lanfranco Food expenditure patterns were analyzed for Hispanic households in the United States. Engel curves for three food categories,total food (TF), food eaten at home (FAH), and food eaten away from home (FAFH),were estimated using a semilogarithmic functional form. The models for TF and FAH were estimated by OLS, using heteroscedasticity consistent estimators. The equation for FAFH was estimated using a two-part model, with the level equation estimated by least squares with corrections for heteroscedasticity, using only the observations for which a positive amount of expenditures on FAFH was reported. The estimated income elasticity of demand for food for Hispanic households were 0.29 for TF, 0.21 for FAH, and 0.49 for FAFH. Household size elasticities were 0.32, 0.40, and 0.07, respectively. Our analysis indicates that Hispanic households devoted a higher proportion of their budget to FAH, 25.8%, than the average American household, while the proportion spent on FAFH was only 3.6%.[EconLit citations: L610.] © 2002 Wiley Periodicals, Inc. [source] A SPATIAL CLIFF-ORD-TYPE MODEL WITH HETEROSKEDASTIC INNOVATIONS: SMALL AND LARGE SAMPLE RESULTS,JOURNAL OF REGIONAL SCIENCE, Issue 2 2010Irani Arraiz ABSTRACT In this paper, we specify a linear Cliff-and-Ord-type spatial model. The model allows for spatial lags in the dependent variable, the exogenous variables, and disturbances. The innovations in the disturbance process are assumed to be heteroskedastic with an unknown form. We formulate multistep GMM/IV-type estimation procedures for the parameters of the model. We also give the limiting distributions for our suggested estimators and consistent estimators for their asymptotic variance-covariance matrices. We conduct a Monte Carlo study to show that the derived large-sample distribution provides a good approximation to the actual small-sample distribution of our estimators. [source] Proportion of non-zero normal means: universal oracle equivalences and uniformly consistent estimatorsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 3 2008Jiashun Jin Summary., Since James and Stein's seminal work, the problem of estimating n normal means has received plenty of enthusiasm in the statistics community. Recently, driven by the fast expansion of the field of large-scale multiple testing, there has been a resurgence of research interest in the n normal means problem. The new interest, however, is more or less concentrated on testing n normal means: to determine simultaneously which means are 0 and which are not. In this setting, the proportion of the non-zero means plays a key role. Motivated by examples in genomics and astronomy, we are particularly interested in estimating the proportion of non-zero means, i.e. given n independent normal random variables with individual means Xj,N(,j,1), j=1,,,n, to estimate the proportion ,n=(1/n) #{j:,j /= 0}. We propose a general approach to construct the universal oracle equivalence of the proportion. The construction is based on the underlying characteristic function. The oracle equivalence reduces the problem of estimating the proportion to the problem of estimating the oracle, which is relatively easier to handle. In fact, the oracle equivalence naturally yields a family of estimators for the proportion, which are consistent under mild conditions, uniformly across a wide class of parameters. The approach compares favourably with recent works by Meinshausen and Rice, and Genovese and Wasserman. In particular, the consistency is proved for an unprecedentedly broad class of situations; the class is almost the largest that can be hoped for without further constraints on the model. We also discuss various extensions of the approach, report results on simulation experiments and make connections between the approach and several recent procedures in large-scale multiple testing, including the false discovery rate approach and the local false discovery rate approach. [source] FDI AND DOMESTIC INVESTMENT IN TAIWAN: AN ENDOGENOUS SWITCHING MODELTHE DEVELOPING ECONOMIES, Issue 4 2007Hui-lin LIN F23; D24; F21; C24 The purpose of this paper is to examine the effect of the FDI decision on domestic investment in the case of Taiwanese manufacturing firms. In addition, we also consider the deferral effect of the FDI decision and the role of firm size. To this end, this paper takes advantage of an endogenous switching model from which consistent estimators are obtained after correcting for the self-selection problem. The empirical results show that the effect of these manufacturing firms' FDI decisions on domestic investment is significant within the firms. Furthermore, a crowding-out effect of FDI on domestic investment is found when Taiwanese firms engage in defensive FDI. Finally, FDI is found to have a positive influence on the domestic investment of the larger firms, while the influence is negative in the case of the smaller firms. [source] Marginal Analysis of Incomplete Longitudinal Binary Data: A Cautionary Note on LOCF ImputationBIOMETRICS, Issue 3 2004Richard J. Cook Summary In recent years there has been considerable research devoted to the development of methods for the analysis of incomplete data in longitudinal studies. Despite these advances, the methods used in practice have changed relatively little, particularly in the reporting of pharmaceutical trials. In this setting, perhaps the most widely adopted strategy for dealing with incomplete longitudinal data is imputation by the "last observation carried forward" (LOCF) approach, in which values for missing responses are imputed using observations from the most recently completed assessment. We examine the asymptotic and empirical bias, the empirical type I error rate, and the empirical coverage probability associated with estimators and tests of treatment effect based on the LOCF imputation strategy. We consider a setting involving longitudinal binary data with longitudinal analyses based on generalized estimating equations, and an analysis based simply on the response at the end of the scheduled follow-up. We find that for both of these approaches, imputation by LOCF can lead to substantial biases in estimators of treatment effects, the type I error rates of associated tests can be greatly inflated, and the coverage probability can be far from the nominal level. Alternative analyses based on all available data lead to estimators with comparatively small bias, and inverse probability weighted analyses yield consistent estimators subject to correct specification of the missing data process. We illustrate the differences between various methods of dealing with drop-outs using data from a study of smoking behavior. [source] | ||||||||||||||||