Mathematics Ph.D. Dissertations

Estimation of Qvf Measurement Error Models Using Empirical Likelihood Method

Date of Award

2009

Document Type

Dissertation

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Mathematics/Mathematical Statistics

First Advisor

Hanfeng Chen (Advisor)

Second Advisor

Christopher Rump (Committee Member)

Third Advisor

Barbara Moses (Committee Member)

Fourth Advisor

John Chen (Committee Member)

Fifth Advisor

Wei Ning (Committee Member)

Abstract

Predictor variables are often contaminated with measurement errors in statistical practice. This may be the case due to bad measurement apparatus or just because the true value of the variable cannot be measured precisely. In the framework of general regression models, measurement errors or misclassifications have very serious consequences in many cases as they lead to bias in the estimated parameters that does not disappear as the sample size goes to infinity. In most cases the estimated effect of the contaminated covariate is attenuated. There are some techniques, regression calibration, simulation extrapolation (SIMEX), and the score function method for correcting effect estimates in the presence of measurement error. These widely used approaches have some restricted applications in many situations, for example, SIMEX is a useful tool for correcting effect estimates in the presences of additive measurement error. The method is especially helpful for complex models with a simple measurement error structure. Score function method is employed only for linear measurement error models. In this dissertation, an inference method has been proposed that accounts for the presence of measurement error in the explanatory variables in both linear and nonlinear models. This approach relies on the consideration of the mean and variance function of the observed data and application of the empirical likelihood approach to those functions, which is referred to as quasi likelihood and variance function (QVF). This proposed approach provides the confidence intervals with high inclusion probability of the unknown regression parameters. Moreover, this method is computationally easy to employ to any measurement error model for correcting bias. In addition, general descriptions and comparisons of the existing methods and the suggested estimation framework with some applications in real life data are discussed. A simulation study is conducted to show the performance of the proposed estimation framework.

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