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Efficient Estimators (efficient + estimator)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Local asymptotic normality and efficient estimation for INAR(p) models

JOURNAL OF TIME SERIES ANALYSIS, Issue 5 2008
Feike C. Drost
Abstract., Integer-valued autoregressive (INAR) processes have been introduced to model non-negative integer-valued phenomena that evolve in time. The distribution of an INAR(p) process is determined by two parameters: a vector of survival probabilities and a probability distribution on the non-negative integers, called an immigration distribution. This paper provides an efficient estimator of the parameters, and in particular, shows that the INAR(p) model has the Local Asymptotic Normality property. [source]

Causal inference with generalized structural mean models

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 4 2003
S. Vansteelandt
Summary., We estimate cause,effect relationships in empirical research where exposures are not completely controlled, as in observational studies or with patient non-compliance and self-selected treatment switches in randomized clinical trials. Additive and multiplicative structural mean models have proved useful for this but suffer from the classical limitations of linear and log-linear models when accommodating binary data. We propose the generalized structural mean model to overcome these limitations. This is a semiparametric two-stage model which extends the structural mean model to handle non-linear average exposure effects. The first-stage structural model describes the causal effect of received exposure by contrasting the means of observed and potential exposure-free outcomes in exposed subsets of the population. For identification of the structural parameters, a second stage ,nuisance' model is introduced. This takes the form of a classical association model for expected outcomes given observed exposure. Under the model, we derive estimating equations which yield consistent, asymptotically normal and efficient estimators of the structural effects. We examine their robustness to model misspecification and construct robust estimators in the absence of any exposure effect. The double-logistic structural mean model is developed in more detail to estimate the effect of observed exposure on the success of treatment in a randomized controlled blood pressure reduction trial with self-selected non-compliance. [source]

Median Regression Models for Longitudinal Data with Dropouts

BIOMETRICS, Issue 2 2009
Grace Y. Yi
Summary Recently, median regression models have received increasing attention. When continuous responses follow a distribution that is quite different from a normal distribution, usual mean regression models may fail to produce efficient estimators whereas median regression models may perform satisfactorily. In this article, we discuss using median regression models to deal with longitudinal data with dropouts. Weighted estimating equations are proposed to estimate the median regression parameters for incomplete longitudinal data, where the weights are determined by modeling the dropout process. Consistency and the asymptotic distribution of the resultant estimators are established. The proposed method is used to analyze a longitudinal data set arising from a controlled trial of HIV disease (Volberding et al., 1990, The New England Journal of Medicine322, 941,949). Simulation studies are conducted to assess the performance of the proposed method under various situations. An extension to estimation of the association parameters is outlined. [source]

Conditional Generalized Estimating Equations for the Analysis of Clustered and Longitudinal Data

BIOMETRICS, Issue 3 2008
Sylvie Goetgeluk
Summary A common and important problem in clustered sampling designs is that the effect of within-cluster exposures (i.e., exposures that vary within clusters) on outcome may be confounded by both measured and unmeasured cluster-level factors (i.e., measurements that do not vary within clusters). When some of these are ill/not accounted for, estimation of this effect through population-averaged models or random-effects models may introduce bias. We accommodate this by developing a general theory for the analysis of clustered data, which enables consistent and asymptotically normal estimation of the effects of within-cluster exposures in the presence of cluster-level confounders. Semiparametric efficient estimators are obtained by solving so-called conditional generalized estimating equations. We compare this approach with a popular proposal by Neuhaus and Kalbfleisch (1998, Biometrics54, 638,645) who separate the exposure effect into a within- and a between-cluster component within a random intercept model. We find that the latter approach yields consistent and efficient estimators when the model is linear, but is less flexible in terms of model specification. Under nonlinear models, this approach may yield inconsistent and inefficient estimators, though with little bias in most practical settings. [source]