Parametric Modeling in the Presence of Measurement Error: Monte Carlo Corrected Scores
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Date
2000-10-23
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Abstract
Parametric estimation is complicated when data are measured with error. The problem of regression modeling when one or more covariates are measured with error is considered in this paper. It is often the case that, evaluated at the observed error-prone data, the unbiased true-data estimating equations yield an inconsistent estimator.The proposed method is a variant of Nakamura's (1990) method of corrected scores and is closely related to the simulation-based algorithm introduced by Cook and Stefanski (1994). The corrected-score method depends critically on finding a function of the observed data having the property that its conditional expectation given the true data equals a true-data, unbiased score function. Nakamura (1990) gives corrected score functions for special cases, but offers no general solution.It is shown that for a certain class of smooth true-data score functions, a corrected score can be determined by Monte Carlo methods, if not analytically. The relationshipbetween the corrected score method and Cook and Stefanski's (1994) simulation method is studied in detail. The properties of the Monte Carlo generated corrected scorefunctions, and of the estimators they define, are also given considerable attention. Special cases are examined in detail, comparing the proposed method with establishedmethods.
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Degree
PhD
Discipline
Statistics
