Minimum distance regression model checking with Berkson measurement errors

Minimum Distance Regression Model Checking with Berkson Measurement Errors

Lack-of-fit testing of a regression model with Berkson measurement error has not been discussed in the literature to date. To fill this void, we propose a class of tests based on minimized integrated square distances between a nonparametric regression function estimator and the parametric model being fitted. We prove asymptotic normality of these test statistics under the null hypothesis and th...

Model Checking in Partial Linear Regression Models with Berkson Measurement Errors

This paper discusses the problem of fitting a parametric model to the nonparametric component in partially linear regression models when covariates in parametric and nonparametric parts are subject to Berkson measurement errors. The proposed test is based on the supremum of a martingale transform of a certain partial sum process of calibrated residuals. Asymptotic null distribution of this tran...

Minimum distance conditional variance function checking in heteroscedastic regression models

Instrumental Variables Regression with Measurement Errors and Multicollinearity in Instruments

In this paper we obtain a consistent estimator when there exist some measurement errors and multicollinearity in the instrumental variables in a two stage least square estimation of parameters. We investigate the asymptotic distribution of the proposed estimator and discuss its properties using some theoretical proofs and a simulation study. A real numerical application is also provided for mor...

Mixtures of Linear Regression with Measurement Errors

Existing research on mixtures of regression models are limited to directly observed predictors. The estimation of mixtures of regression for measurement error data imposes challenges for statisticians. For linear regression models with measurement error data, the naive ordinary least squares method, which directly substitutes the observed surrogates for the unobserved error-prone variables, yie...