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Nonparametric Estimation (nonparametric + estimation)
Selected AbstractsNONPARAMETRIC ESTIMATION OF CONDITIONAL CUMULATIVE HAZARDS FOR MISSING POPULATION MARKSAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 1 2010Dipankar Bandyopadhyay Summary A new function for the competing risks model, the conditional cumulative hazard function, is introduced, from which the conditional distribution of failure times of individuals failing due to cause,j,can be studied. The standard Nelson,Aalen estimator is not appropriate in this setting, as population membership (mark) information may be missing for some individuals owing to random right-censoring. We propose the use of imputed population marks for the censored individuals through fractional risk sets. Some asymptotic properties, including uniform strong consistency, are established. We study the practical performance of this estimator through simulation studies and apply it to a real data set for illustration. [source] Nonparametric Estimation of Nonadditive Random FunctionsECONOMETRICA, Issue 5 2003Rosa L. Matzkin We present estimators for nonparametric functions that are nonadditive in unobservable random terms. The distributions of the unobservable random terms are assumed to be unknown. We show that when a nonadditive, nonparametric function is strictly monotone in an unobservable random term, and it satisfies some other properties that may be implied by economic theory, such as homogeneity of degree one or separability, the function and the distribution of the unobservable random term are identified. We also present convenient normalizations, to use when the properties of the function, other than strict monotonicity in the unobservable random term, are unknown. The estimators for the nonparametric function and for the distribution of the unobservable random term are shown to be consistent and asymptotically normal. We extend the results to functions that depend on a multivariate random term. The results of a limited simulation study are presented. [source] Optimal Nonparametric Estimation of First-price AuctionsECONOMETRICA, Issue 3 2000Emmanuel Guerre This paper proposes a general approach and a computationally convenient estimation procedure for the structural analysis of auction data. Considering first-price sealed-bid auction models within the independent private value paradigm, we show that the underlying distribution of bidders' private values is identified from observed bids and the number of actual bidders without any parametric assumptions. Using the theory of minimax, we establish the best rate of uniform convergence at which the latent density of private values can be estimated nonparametrically from available data. We then propose a two-step kernel-based estimator that converges at the optimal rate. [source] Equilibrium Search with Continuous Productivity Dispersion: Theory and Nonparametric EstimationINTERNATIONAL ECONOMIC REVIEW, Issue 2 2000Christian Bontemps In this article we develop an equilibrium search model with a continuous distribution of firm productivity types within a given labor market. We characterize equilibrium, derive expressions for the endogenous equilibrium wage distributions, and characterize the set of wage distributions that can be generated by the model. We develop a structural nonparametric estimation method for the productivity distribution. We estimate the model using French longitudinal survey data on labor supply, and we compare the results with those from a French panel data set of firms. The results are informative on the degree to which firms exploit search frictions. [source] Nonparametric Estimation and Testing in Panels of Intercorrelated Time SeriesJOURNAL OF TIME SERIES ANALYSIS, Issue 6 2004Vidar Hjellvik Abstract., We consider nonparametric estimation and testing of linearity in a panel of intercorrelated time series. We place the emphasis on the situation where there are many time series in the panel but few observations for each of the series. The intercorrelation is described by a latent process, and a conditioning argument involving this process plays an important role in deriving the asymptotic theory. To be accurate the asymptotic distribution of the test functional of linearity requires a very large number of observations, and bootstrapping gives much better finite sample results. A number of simulation experiments and an illustration on a real data set are included. [source] Nonparametric Estimation in a Markov "Illness,Death" Process from Interval Censored Observations with Missing Intermediate Transition StatusBIOMETRICS, Issue 1 2009Halina Frydman Summary In many clinical trials patients are intermittently assessed for the transition to an intermediate state, such as occurrence of a disease-related nonfatal event, and death. Estimation of the distribution of nonfatal event free survival time, that is, the time to the first occurrence of the nonfatal event or death, is the primary focus of the data analysis. The difficulty with this estimation is that the intermittent assessment of patients results in two forms of incompleteness: the times of occurrence of nonfatal events are interval censored and, when a nonfatal event does not occur by the time of the last assessment, a patient's nonfatal event status is not known from the time of the last assessment until the end of follow-up for death. We consider both forms of incompleteness within the framework of an "illness,death" model. We develop nonparametric maximum likelihood (ML) estimation in an "illness,death" model from interval-censored observations with missing status of intermediate transition. We show that the ML estimators are self-consistent and propose an algorithm for obtaining them. This work thus provides new methodology for the analysis of incomplete data that arise from clinical trials. We apply this methodology to the data from a recently reported cancer clinical trial (Bonner et al., 2006, New England Journal of Medicine354, 567,578) and compare our estimation results with those obtained using a Food and Drug Administration recommended convention. [source] Bayesian Nonparametric Estimation of Continuous Monotone Functions with Applications to Dose,Response AnalysisBIOMETRICS, Issue 1 2009Björn Bornkamp Summary In this article, we consider monotone nonparametric regression in a Bayesian framework. The monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions, and a general random probability measure is assumed as the prior for the mixing distribution. We investigate the choice of the underlying parametric distribution function and find that the two-sided power distribution function is well suited both from a computational and mathematical point of view. The model is motivated by traditional nonlinear models for dose,response analysis, and provides possibilities to elicitate informative prior distributions on different aspects of the curve. The method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose,response analysis. [source] Nonparametric Estimation in a Cure Model with Random Cure TimesBIOMETRICS, Issue 1 2001Rebecca A. Betensky Summary. Acute respiratory distress syndrome (ARDS) is a life-threatening acute condition that sometimes follows pneumonia or surgery. Patients who recover and leave the hospital are considered to have been cured at the time they leave the hospital. These data differ from typical data in which cure is a possibility: death times are not observed for patients who are cured and cure times are observed and vary among patients. Here we apply a competing risks model to these data and show it to be equivalent to a mixture model, the more common approach for cure data. Further, we derive an estimator for the variance of the cumulative incidence function from the competing risks model, and thus for the cure rate, based on elementary calculations. We compare our variance estimator to Gray's (1988, Annals of Statistics16, 1140,1154) estimator, which is based on counting process theory. We find our estimator to be slightly more accurate in small samples. We apply these results to data from an ARDS clinical trial. [source] Nonparametric Estimation for the Three-Stage Irreversible Illness,Death ModelBIOMETRICS, Issue 3 2000Somnath Datta Summary. In this paper, we present new nonparametric estimators of the stage-occupation probabilities in the three-stage irreversible illness-death model. These estimators use a fractional risk set and a reweighting approach and are valid under stage-dependent censoring. Using a simulated data set, we compare the behavior of our estimators with previously proposed estimators. We also apply our estimators to data on time to Pneumocystis pneumonia and death obtained from an AIDS cohort study. [source] Nonparametric estimation of a hedonic price functionJOURNAL OF APPLIED ECONOMETRICS, Issue 3 2007Christopher F. Parmeter Rosen's (1974) theory of hedonic prices is implemented econometrically using recently developed nonparametric techniques to examine the influence of qualitative factors on the price of a house. Our ability to smooth categorical variables leads to greater generalization in the valuation process and provides a canvas for interactions between categorical and continuous variables that is difficult to exploit in parametric and semiparametric models. This is illustrated with a replication of a previously used partially linear model specification. Copyright © 2007 John Wiley & Sons, Ltd. [source] Nonparametric Varying-Coefficient Models for the Analysis of Longitudinal DataINTERNATIONAL STATISTICAL REVIEW, Issue 3 2002Colin O. Wu Summary Longitudinal methods have been widely used in biomedicine and epidemiology to study the patterns of time-varying variables, such as disease progression or trends of health status. Data sets of longitudinal studies usually involve repeatedly measured outcomes and covariates on a set of randomly chosen subjects over time. An important goal of statistical analyses is to evaluate the effects of the covariates, which may or may not depend on time, on the outcomes of interest. Because fully parametric models may be subject to model misspecification and completely unstructured nonparametric models may suffer from the drawbacks of "curse of dimensionality", the varying-coefficient models are a class of structural nonparametric models which are particularly useful in longitudinal analyses. In this article, we present several important nonparametric estimation and inference methods for this class of models, demonstrate the advantages, limitations and practical implementations of these methods in different longitudinal settings, and discuss some potential directions of further research in this area. Applications of these methods are illustrated through two epidemiological examples. Résumé Modèles non-paramétriques à coefficients variables pour l'analyse de données longitudinales Les méthodes longitudinales ont été largement utilisées en biomédecine et en épidémiologie pour étudier les modèles de variables variant dans le temps, du type progression de maladie ou tendances détat de santé. Les ensembles de données d'études longitudinales comprennent généralement des ésultats de mesures répétées et des covariables sur un ensemble de sujets choisis au hasard dans le temps. Un objectif important des analyses statistiques consisteàévaluer les effets des covariables, qui peuvent ou non dépendre du temps, sur les résultats d'intérêt. Du fait que des modèles entièrement paramétriques peuvent faire l'objet d'erreur de spécification de modèle et que des modèles non-paramétriques totalement non-structurés peuvent souffrir des inconvénients de la «malédiction de dimensionnalité», les modèles à coefficients variables sont une classe de modèles structurels non-paramétriques particulièrement utiles dans les analyses longitudinales. Dans cet article, on présente plusieurs estimations non-paramétriques importantes, ainsi que des méthodes d'inférence pour cette classe de modéles, on démontre les avantages, limites et mises en ,uvre pratiques de ces méthodes dans différents contextes longitudinaux et l'on traite de certaines directions possibles pour de plus amples recherches dans ce domaine. Des applications de ces méthodes sont illustrées à travers deux exemples épidémiologiques. [source] ESTIMATION AND HYPOTHESIS TESTING FOR NONPARAMETRIC HEDONIC HOUSE PRICE FUNCTIONSJOURNAL OF REGIONAL SCIENCE, Issue 3 2010Daniel P. McMillen ABSTRACT In contrast to the rigid structure of standard parametric hedonic analysis, nonparametric estimators control for misspecified spatial effects while using highly flexible functional forms. Despite these advantages, nonparametric procedures are still not used extensively for spatial data analysis due to perceived difficulties associated with estimation and hypothesis testing. We demonstrate that nonparametric estimation is feasible for large datasets with many independent variables, offering statistical tests of individual covariates and tests of model specification. We show that fixed parameterization of distance to the nearest rapid transit line is a misspecification and that pricing of access to this amenity varies across neighborhoods within Chicago. [source] A light-tailed conditionally heteroscedastic model with applications to river flowsJOURNAL OF TIME SERIES ANALYSIS, Issue 1 2008Péter Elek Abstract., A conditionally heteroscedastic model, different from the more commonly used autoregressive moving average,generalized autoregressive conditionally heteroscedastic (ARMA-GARCH) processes, is established and analysed here. The time-dependent variance of innovations passing through an ARMA filter is conditioned on the lagged values of the generated process, rather than on the lagged innovations, and is defined to be asymptotically proportional to those past values. Designed this way, the model incorporates certain feedback from the modelled process, the innovation is no longer of GARCH type, and all moments of the modelled process are finite provided the same is true for the generating noise. The article gives the condition of stationarity, and proves consistency and asymptotic normality of the Gaussian quasi-maximum likelihood estimator of the variance parameters, even though the estimated parameters of the linear filter contain an error. An analysis of six diurnal water discharge series observed along Rivers Danube and Tisza in Hungary demonstrates the usefulness of such a model. The effect of lagged river discharge turns out to be highly significant on the variance of innovations, and nonparametric estimation approves its approximate linearity. Simulations from the new model preserve well the probability distribution, the high quantiles, the tail behaviour and the high-level clustering of the original series, further justifying model choice. [source] Nonparametric Estimation and Testing in Panels of Intercorrelated Time SeriesJOURNAL OF TIME SERIES ANALYSIS, Issue 6 2004Vidar Hjellvik Abstract., We consider nonparametric estimation and testing of linearity in a panel of intercorrelated time series. We place the emphasis on the situation where there are many time series in the panel but few observations for each of the series. The intercorrelation is described by a latent process, and a conditioning argument involving this process plays an important role in deriving the asymptotic theory. To be accurate the asymptotic distribution of the test functional of linearity requires a very large number of observations, and bootstrapping gives much better finite sample results. A number of simulation experiments and an illustration on a real data set are included. [source] Prediction and nonparametric estimation for time series with heavy tailsJOURNAL OF TIME SERIES ANALYSIS, Issue 3 2002PETER HALL Motivated by prediction problems for time series with heavy-tailed marginal distributions, we consider methods based on `local least absolute deviations' for estimating a regression median from dependent data. Unlike more conventional `local median' methods, which are in effect based on locally fitting a polynomial of degree 0, techniques founded on local least absolute deviations have quadratic bias right up to the boundary of the design interval. Also in contrast to local least-squares methods based on linear fits, the order of magnitude of variance does not depend on tail-weight of the error distribution. To make these points clear, we develop theory describing local applications to time series of both least-squares and least-absolute-deviations methods, showing for example that, in the case of heavy-tailed data, the conventional local-linear least-squares estimator suffers from an additional bias term as well as increased variance. [source] Functional Coefficient Autoregressive Models: Estimation and Tests of HypothesesJOURNAL OF TIME SERIES ANALYSIS, Issue 2 2001Rong Chen In this paper, we study nonparametric estimation and hypothesis testing procedures for the functional coefficient AR (FAR) models of the form Xt=f1(Xt,d)Xt, 1+ ... +fp(Xt,d)Xt,p+,t, first proposed by Chen and Tsay (1993). As a direct generalization of the linear AR model, the FAR model is a rich class of models that includes many useful parametric nonlinear time series models such as the threshold AR models of Tong (1983) and exponential AR models of Haggan and Ozaki (1981). We propose a local linear estimation procedure for estimating the coefficient functions and study its asymptotic properties. In addition, we propose two testing procedures. The first one tests whether all the coefficient functions are constant, i.e. whether the process is linear. The second one tests if all the coefficient functions are continuous, i.e. if any threshold type of nonlinearity presents in the process. The results of some simulation studies as well as a real example are presented. [source] On inference for a semiparametric partially linear regression model with serially correlated errorsTHE CANADIAN JOURNAL OF STATISTICS, Issue 4 2007Jinhong You Abstract The authors consider a semiparametric partially linear regression model with serially correlated errors. They propose a new way of estimating the error structure which has the advantage that it does not involve any nonparametric estimation. This allows them to develop an inference procedure consisting of a bandwidth selection method, an efficient semiparametric generalized least squares estimator of the parametric component, a goodness-of-fit test based on the bootstrap, and a technique for selecting significant covariates in the parametric component. They assess their approach through simulation studies and illustrate it with a concrete application. L'inférence dans le cadre d'un modèle de régression semiparamétrique partiellement linéaire à termes d'erreur corrélés en série Les auteurs s'intéressent à un modèle de régression semiparamétrique partiellement linéaire à termes d'erreur corrélés en série. Ils proposent une façon originale d'estimer la structure d'erreur qui a l'avantage de ne faire intervenir aucune estimation non paramétrique. Ceci leur permet de développer une procédure d'inférence comportant un choix de fen,tre, l'emploi de la méthode des moindres carrés généralisés pour l'estimation semiparamétrique efficace de la composante paramétrique, un test d'adéquation fondé sur le rééchantillonnage et une technique de sélection des covariables significatives de la composante paramétrique. Ils évaluent leur approche par voie de simulation et en donnent une illustration concrète. [source] Genome Scanning Tests for Comparing Amino Acid Sequences Between GroupsBIOMETRICS, Issue 1 2008Peter B. Gilbert Summary Consider a placebo-controlled preventive HIV vaccine efficacy trial. An HIV amino acid sequence is measured from each volunteer who acquires HIV, and these sequences are aligned together with the reference HIV sequence represented in the vaccine. We develop genome scanning methods to identify positions at which the amino acids in infected vaccine recipient sequences either (A) are more divergent from the reference amino acid than the amino acids in infected placebo recipient sequences or (B) have a different frequency distribution than the placebo sequences, irrespective of a reference amino acid. We consider t -test-type statistics for problem A and Euclidean, Mahalanobis, and Kullback,Leibler-type statistics for problem B. The test statistics incorporate weights to reflect biological information contained in different amino acid positions and mismatches. Position-specific p -values are obtained by approximating the null distribution of the statistics either by a permutation procedure or by a nonparametric estimation. A permutation method is used to estimate a cut-off p -value to control the per comparison error rate at a prespecified level. The methods are examined in simulations and are applied to two HIV examples. The methods for problem B address the general problem of comparing discrete frequency distributions between groups in a high-dimensional data setting. [source] Bayesian Nonparametric Modeling Using Mixtures of Triangular DistributionsBIOMETRICS, Issue 2 2001F. Perron Summary. Nonparametric modeling is an indispensable tool in many applications and its formulation in an hierarchical Bayesian context, using the entire posterior distribution rather than particular expectations, increases its flexibility. In this article, the focus is on nonparametric estimation through a mixture of triangular distributions. The optimality of this methodology is addressed and bounds on the accuracy of this approximation are derived. Although our approach is more widely applicable, we focus for simplicity on estimation of a monotone nondecreasing regression on [0, 1] with additive error, effectively approximating the function of interest by a function having a piecewise linear derivative. Computationally accessible methods of estimation are described through an amalgamation of existing Markov chain Monte Carlo algorithms. Simulations and examples illustrate the approach. [source] | |||||||||||||