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Regression Estimator (regression + estimator)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Efficiency of Functional Regression Estimators for Combining Multiple Laser Scans of cDNA Microarrays

BIOMETRICAL JOURNAL, Issue 1 2009
C. A. Glasbey
Abstract The first stage in the analysis of cDNA microarray data is estimation of the level of expression of each gene, from laser scans of hybridised microarrays. Typically, data are used from a single scan, although, if multiple scans are available, there is the opportunity to reduce sampling error by using all of them. Combining multiple laser scans can be formulated as multivariate functional regression through the origin. Maximum likelihood estimation fails, but many alternative estimators exist, one of which is to maximise the likelihood of a Gaussian structural regression model. We show by simulation that, surprisingly, this estimator is efficient for our problem, even though the distribution of gene expression values is far from Gaussian. Further, it performs well if errors have a heavier tailed distribution or the model includes intercept terms, but not necessarily in other regions of parameter space. Finally, we show that by combining multiple laser scans we increase the power to detect differential expression of genes. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Nonresponse weighting adjustment using estimated response probability

THE CANADIAN JOURNAL OF STATISTICS, Issue 4 2007
Jae Kwang Kim
Abstract To reduce nonresponse bias in sample surveys, a method of nonresponse weighting adjustment is often used which consists of multiplying the sampling weight of the respondent by the inverse of the estimated response probability. The authors examine the asymptotic properties of this estimator. They prove that it is generally more efficient than an estimator which uses the true response probability, provided that the parameters which govern this probability are estimated by maximum likelihood. The authors discuss variance estimation methods that account for the effect of using the estimated response probability; they compare their performances in a small simulation study. They also discuss extensions to the regression estimator. Correction de la non-réponse par repondération au moyen d'une estimation de la probabilité de réponse Pour réduire le biais d, à la non-réponse dans les enqu,tes, on fait souvent appel à une méthode d'ajustement dans laquelle le poids de sondage de chaque répondant est multiplié par l'inverse d'une estimation de la probabilité de réponse. Les auteurs étudient les propriétés asymptotiques de cet estimateur. Ils démontrent qu'il est généralement plus efficace que celui qui fait intervenir la probabilité de réponse théorique, pourvu que les paramètres qui régissent cette probabilité soient estimés par vraisemblance maximale. Les auteurs évoquent diverses méthodes d'estimation de la variance qui tiennent compte du fait que la probabilité de réponse est estimée; ils en comparent la performance dans le cadre d'une petite étude de simulation. Ils étendent aussi leurs résultats à l'estimateur obtenu par régression. [source]

A note on penalized minimum distance estimation in nonparametric regression

THE CANADIAN JOURNAL OF STATISTICS, Issue 3 2003
Florentina Bunea
Abstract The authors introduce a penalized minimum distance regression estimator. They show the estimator to balance, among a sequence of nested models of increasing complexity, the L1 -approximation error of each model class and a penalty term which reflects the richness of each model and serves as a upper bound for the estimation error. Les auteurs présentent un nouvel estimateur de régression obtenu par minimisation d'une distance pénalisée. Ils montrent que pour une suite de modèles embo,tés à complexité croissante, cet estimateur offre un bon compromis entre l'erreur d'approximation L1 de chaque classe de modèles et un terme de pénalisation permettant à la fois de refléter la richesse de chaque modèle et de majorer l'erreur d'estimation. [source]

Variance estimation for two-phase stratified sampling

THE CANADIAN JOURNAL OF STATISTICS, Issue 4 2000
David A. Binder
Abstract The authors consider variance estimation for the generalized regression estimator in a two-phase context when the first-phase sample has been restratified using information gathered from the first-phase sample. Simple computational expressions for variance estimation are provided for the double expansion estimator and the reweighted expansion estimator of Kott & Stukel (1997). These estimators are compared using data from the Canadian Retail Commodity Survey. RÉSUMÉ Les auteurs s'intéressent à l'estimation de la variance de l'estimateur de régression généralisé pour un plan de sondage à deux phases dans le cas où l'échantillon de première phase a été stratifié à partir d'information auxiliaire disponible pour cette phase. Des expressions simples sont fournies pour l'estimation de la variance de l'estimateur doublement dilaté et de l'estimateur repondéré de Kott & Stukel (1997). Ces estimations sont companées au moyen de données provenant de l'Enqu,te canadienne sur les marchandises de détail [source]

Structural Nested Mean Models for Assessing Time-Varying Effect Moderation

BIOMETRICS, Issue 1 2010
Daniel Almirall
Summary This article considers the problem of assessing causal effect moderation in longitudinal settings in which treatment (or exposure) is time varying and so are the covariates said to moderate its effect.,Intermediate causal effects,that describe time-varying causal effects of treatment conditional on past covariate history are introduced and considered as part of Robins' structural nested mean model. Two estimators of the intermediate causal effects, and their standard errors, are presented and discussed: The first is a proposed two-stage regression estimator. The second is Robins' G-estimator. The results of a small simulation study that begins to shed light on the small versus large sample performance of the estimators, and on the bias,variance trade-off between the two estimators are presented. The methodology is illustrated using longitudinal data from a depression study. [source]

Central limit theorems for nonparametric estimators with real-time random variables

JOURNAL OF TIME SERIES ANALYSIS, Issue 5 2010
Tae Yoon Kim
Primary 62G07; 62F12; Secondary 62M05 C13; C14 In this article, asymptotic theories for nonparametric methods are studied when they are applied to real-time data. In particular, we derive central limit theorems for nonparametric density and regression estimators. For this we formally introduce a sequence of real-time random variables indexed by a parameter related to fine gridding of time domain (or fine discretization). Our results show that the impact of fine gridding is greater in the density estimation case in the sense that strong dependence due to fine gridding severely affects the major strength of nonparametric density estimator (or its data-adaptive property). In addition, we discuss some issues about nonparametric regression model with fine gridding of time domain. [source]

Robust estimation of the SUR model

THE CANADIAN JOURNAL OF STATISTICS, Issue 2 2000
Martin Bilodeau
Abstract This paper proposes robust regression to solve the problem of outliers in seemingly unrelated regression (SUR) models. The authors present an adaptation of S -estimators to SUR models. S -estimators are robust, have a high breakdown point and are much more efficient than other robust regression estimators commonly used in practice. Furthermore, modifications to Ruppert's algorithm allow a fast evaluation of them in this context. The classical example of U.S. corporations is revisited, and it appears that the procedure gives an interesting insight into the problem. Les auteurs proposent une méthode de régression robuste pour résoudre le problème des valeurs aberrantes dans les modèles SUR. Ils adaptent les S -estimateurs dans les modèles SUR. Les S -estimateurs sont robustes, ont un haut point de rupture et sont beaucoup plus efficaces que les autres estimateurs robustes de régression couramment utilisés en pratique. De plus, une modification de l'algorithme de Ruppert permet une évaluation rapide de ces estimateurs dans ce contexte. La procédure donne une compréhension intéressante d'un problème classique portant sur des compagnies américaines. [source]

VARIANCE ESTIMATION IN TWO-PHASE SAMPLING

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2009
M.A. Hidiroglou
Summary Two-phase sampling is often used for estimating a population total or mean when the cost per unit of collecting auxiliary variables, x, is much smaller than the cost per unit of measuring a characteristic of interest, y. In the first phase, a large sample s1 is drawn according to a specific sampling design p(s1), and auxiliary data x are observed for the units i,s1. Given the first-phase sample s1, a second-phase sample s2 is selected from s1 according to a specified sampling design {p(s2,s1) }, and (y, x) is observed for the units i,s2. In some cases, the population totals of some components of x may also be known. Two-phase sampling is used for stratification at the second phase or both phases and for regression estimation. Horvitz,Thompson-type variance estimators are used for variance estimation. However, the Horvitz,Thompson (Horvitz & Thompson, J. Amer. Statist. Assoc. 1952) variance estimator in uni-phase sampling is known to be highly unstable and may take negative values when the units are selected with unequal probabilities. On the other hand, the Sen,Yates,Grundy variance estimator is relatively stable and non-negative for several unequal probability sampling designs with fixed sample sizes. In this paper, we extend the Sen,Yates,Grundy (Sen, J. Ind. Soc. Agric. Statist. 1953; Yates & Grundy, J. Roy. Statist. Soc. Ser. B 1953) variance estimator to two-phase sampling, assuming fixed first-phase sample size and fixed second-phase sample size given the first-phase sample. We apply the new variance estimators to two-phase sampling designs with stratification at the second phase or both phases. We also develop Sen,Yates,Grundy-type variance estimators of the two-phase regression estimators that make use of the first-phase auxiliary data and known population totals of some of the auxiliary variables. [source]