SFB 303 Discussion Paper No. A - 236

Author: Carroll, Raymond J.
Title: Semiparametric Estimation in Logistic Measurement Error Models
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 assumptions are 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.
Keywords: Bandwidth Selection, Density Estimation, Errors-in-Variables, Generalized Linear Models, Kernel Regression, Logistic Regression, Maximum Likelihood, Measurement Errors Models, Nonparametric Regression, Probit Regression
JEL-Classification-Number: 132
Creation-Date: May 1989
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