Estimators For Generalized Linear Measurement Error Models With Interaction Terms
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2001-10-22
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Abstract
The primary objectives of this research are to develop andstudy estimators for generalized linear measurement errormodels when the mean function contains error-free predictorsas well as predictors measured with error and interactions between error-free and error-prone predictors. Attention is restricted to generalized linear models in canonical form with independent additive Gaussian measurement error in the error-prone predictors.Estimators appropriate for the functional (Fuller, 1987, Ch.1) version of the measurement error model are derived and studied. The estimators are also appropriate in the structural version of the model and thus the methods developed in this research are functional in the sense of Carroll, Ruppert and Stefanski (1995, Ch. 6).The primary approach to the development of estimators in this research is the conditional-score method proposed byStefanski and Carroll (1987) and described by Carroll et al.(1995, Ch. 6). Sufficient statistics for the unobserved predictors are obtained and the conditional distribution of the observed data given these sufficient statistics is derived. The latter admits unbiased score functions that arefree of the nuisance parameters (the unobserved predictors) and are used to construct unbiased estimating equations for model parameters.Estimators for the parameters of the model of interest are also derived using the corrected approach proposed by Nakamura (1990) and Stefanski (1989). These are also functional estimators in the sense of Carroll et al. (1995, Ch. 6) that are less dependent on the exponential-family model assumptions and thus provide a benchmark against whichto compare the conditional-score estimators.Large-sample distribution approximations for both theconditional-score and corrected-score estimators are derivedand the performance of the estimators and the adequacy of the large-sample distribution theory are studied via Monte Carlo simulation.
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PhD
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Statistics
