Resulting Estimators (resulting + estimator)

Distribution by Scientific Domains


Selected Abstracts


Likelihood analysis of joint marginal and conditional models for longitudinal categorical data

THE CANADIAN JOURNAL OF STATISTICS, Issue 2 2009
Baojiang Chen
MSC 2000: Primary 62H12; secondary 62F10 Abstract The authors develop a Markov model for the analysis of longitudinal categorical data which facilitates modelling both marginal and conditional structures. A likelihood formulation is employed for inference, so the resulting estimators enjoy the optimal properties such as efficiency and consistency, and remain consistent when data are missing at random. Simulation studies demonstrate that the proposed method performs well under a variety of situations. Application to data from a smoking prevention study illustrates the utility of the model and interpretation of covariate effects. The Canadian Journal of Statistics © 2009 Statistical Society of Canada Les auteurs développent un modèle de Markov pour l'analyse de données catégorielles longitudinales facilitant la représentation des structures marginales et conditionnelles. L'inférence est basée sur une fonction de vraisemblance afin d'obtenir des estimateurs efficaces, cohérents et qui le demeurent lorsqu'il y a des données manquantes au hasard. Des études de simulation montrent que la méthode proposée se comporte bien dans les différents scénarios considérés. L'application à des données provenant d'une étude sur la lutte contre le tabagisme illustre bien l'utilité de ce modèle et permet une interprétation des effets des covariables. La revue canadienne de statistique © 2009 Société statistique du Canada [source]


ROBUST ESTIMATION OF SMALL-AREA MEANS AND QUANTILES

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2010
Nikos Tzavidis
Summary Small-area estimation techniques have typically relied on plug-in estimation based on models containing random area effects. More recently, regression M-quantiles have been suggested for this purpose, thus avoiding conventional Gaussian assumptions, as well as problems associated with the specification of random effects. However, the plug-in M-quantile estimator for the small-area mean can be shown to be the expected value of this mean with respect to a generally biased estimator of the small-area cumulative distribution function of the characteristic of interest. To correct this problem, we propose a general framework for robust small-area estimation, based on representing a small-area estimator as a functional of a predictor of this small-area cumulative distribution function. Key advantages of this framework are that it naturally leads to integrated estimation of small-area means and quantiles and is not restricted to M-quantile models. We also discuss mean squared error estimation for the resulting estimators, and demonstrate the advantages of our approach through model-based and design-based simulations, with the latter using economic data collected in an Australian farm survey. [source]


Estimation in Semiparametric Transition Measurement Error Models for Longitudinal Data

BIOMETRICS, Issue 3 2009
Wenqin Pan
Summary We consider semiparametric transition measurement error models for longitudinal data, where one of the covariates is measured with error in transition models, and no distributional assumption is made for the underlying unobserved covariate. An estimating equation approach based on the pseudo conditional score method is proposed. We show the resulting estimators of the regression coefficients are consistent and asymptotically normal. We also discuss the issue of efficiency loss. Simulation studies are conducted to examine the finite-sample performance of our estimators. The longitudinal AIDS Costs and Services Utilization Survey data are analyzed for illustration. [source]


Joint Modeling and Analysis of Longitudinal Data with Informative Observation Times

BIOMETRICS, Issue 2 2009
Yu Liang
Summary In analysis of longitudinal data, it is often assumed that observation times are predetermined and are the same across study subjects. Such an assumption, however, is often violated in practice. As a result, the observation times may be highly irregular. It is well known that if the sampling scheme is correlated with the outcome values, the usual statistical analysis may yield bias. In this article, we propose joint modeling and analysis of longitudinal data with possibly informative observation times via latent variables. A two-step estimation procedure is developed for parameter estimation. We show that the resulting estimators are consistent and asymptotically normal, and that the asymptotic variance can be consistently estimated using the bootstrap method. Simulation studies and a real data analysis demonstrate that our method performs well with realistic sample sizes and is appropriate for practical use. [source]


Test of Marginal Compatibility and Smoothing Methods for Exchangeable Binary Data with Unequal Cluster Sizes

BIOMETRICS, Issue 1 2007
Zhen Pang
Summary Exchangeable binary data are often collected in developmental toxicity and other studies, and a whole host of parametric distributions for fitting this kind of data have been proposed in the literature. While these distributions can be matched to have the same marginal probability and intra-cluster correlation, they can be quite different in terms of shape and higher-order quantities of interest such as the litter-level risk of having at least one malformed fetus. A sensible alternative is to fit a saturated model (Bowman and George, 1995, Journal of the American Statistical Association90, 871,879) using the expectation-maximization (EM) algorithm proposed by Stefanescu and Turnbull (2003, Biometrics59, 18,24). The assumption of compatibility of marginal distributions is often made to link up the distributions for different cluster sizes so that estimation can be based on the combined data. Stefanescu and Turnbull proposed a modified trend test to test this assumption. Their test, however, fails to take into account the variability of an estimated null expectation and as a result leads to inaccurate p -values. This drawback is rectified in this article. When the data are sparse, the probability function estimated using a saturated model can be very jagged and some kind of smoothing is needed. We extend the penalized likelihood method (Simonoff, 1983, Annals of Statistics11, 208,218) to the present case of unequal cluster sizes and implement the method using an EM-type algorithm. In the presence of covariate, we propose a penalized kernel method that performs smoothing in both the covariate and response space. The proposed methods are illustrated using several data sets and the sampling and robustness properties of the resulting estimators are evaluated by simulations. [source]