Electronic Journal of Statistics

Estimation via corrected scores in general semiparametric regression models with error-prone covariates

Arnab Maity and Tatiyana V. Apanasovich

Full-text: Open access

Abstract

This paper considers the problem of estimation in a general semiparametric regression model when error-prone covariates are modeled parametrically while covariates measured without error are modeled nonparametrically. To account for the effects of measurement error, we apply a correction to a criterion function. The specific form of the correction proposed allows Monte Carlo simulations in problems for which the direct calculation of a corrected criterion is difficult. Therefore, in contrast to methods that require solving integral equations of possibly multiple dimensions, as in the case of multiple error-prone covariates, we propose methodology which offers a simple implementation. The resulting methods are functional, they make no assumptions about the distribution of the mismeasured covariates. We utilize profile kernel and backfitting estimation methods and derive the asymptotic distribution of the resulting estimators. Through numerical studies we demonstrate the applicability of proposed methods to Poisson, logistic and multivariate Gaussian partially linear models. We show that the performance of our methods is similar to a computationally demanding alternative. Finally, we demonstrate the practical value of our methods when applied to Nevada Test Site (NTS) Thyroid Disease Study data.

Article information

Source
Electron. J. Statist., Volume 5 (2011), 1424-1449.

Dates
First available in Project Euclid: 4 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1320416980

Digital Object Identifier
doi:10.1214/11-EJS647

Mathematical Reviews number (MathSciNet)
MR2851685

Zentralblatt MATH identifier
1271.62087

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties

Keywords
Generalized estimating equations generalized linear mixed models kernel method measurement error Monte Carlo Corrected Score semiparametric regression

Citation

Maity, Arnab; Apanasovich, Tatiyana V. Estimation via corrected scores in general semiparametric regression models with error-prone covariates. Electron. J. Statist. 5 (2011), 1424--1449. doi:10.1214/11-EJS647. https://projecteuclid.org/euclid.ejs/1320416980


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