Abstract

In statistical analysis or supervised learning, classification has been an attractive topic. Typically, a main goal is to adopt predictors to characterize the primarily interested binary random variables. To model a binary response and predictors, parametric structures, such as logistic regression or probit models, are perhaps commonly used approaches. However, due to the convenience of data collection, a large amount of variables with inevitability of measurement error in variables becomes ubiquitous. These complex features make data analysis become challenging, and conventional methods are invalid. To address those concerns, we propose a valid inferential method to deal with measurement error and handle variable selection simultaneously. Specifically, we focus on logistic regression or probit models, and propose error-eliminated estimating functions by incorporating corrected responses and predictors. After that, we develop the boosting procedure with proposed estimating functions accommodated to do variable selection and estimation. To justify the proposed method, we rigorously establish the theoretical results. Through numerical studies, we find that the proposed method accurately retains informative predictors and gives precise estimators, and its performance is generally better than that without measurement error correction.