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Semiparametric Estimation in Logistic Measurement Error Models

R. J. Carroll and M. P. Wand
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 53, No. 3 (1991), pp. 573-585
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2345587
Page Count: 13
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Semiparametric Estimation in Logistic Measurement Error Models
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Abstract

We describe semiparametric estimation and inference in a logistic regression model with measurement error in the predictors. The particular measurement error model consists of a primary data set in which only the response Y and a fallible surrogate W of the true predictor X are observed, plus a smaller validation data set for which (Y, X, W) are observed. Except for the underlying assumption of a logistic model in the true predictor, no parametric distributional assumption is made about the true predictor or its surrogate. We develop a semiparametric parameter estimate of the logistic regression parameter which is asymptotically normally distributed and computationally feasible. The estimate relies on kernel regression techniques. For scalar predictors, by a detailed analysis of the mean-squared error of the parameter estimate, we obtain a representation for an optimal bandwidth.

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