Overview of High-Dimensional Measurement Error Regression Models

Jingxuan Luo, Lili Yue and Gaorong Li ()
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Jingxuan Luo: School of Statistics, Beijing Normal University, Beijing 100875, China
Lili Yue: School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China
Gaorong Li: School of Statistics, Beijing Normal University, Beijing 100875, China

Mathematics, 2023, vol. 11, issue 14, 1-22

Abstract: High-dimensional measurement error data are becoming more prevalent across various fields. Research on measurement error regression models has gained momentum due to the risk of drawing inaccurate conclusions if measurement errors are ignored. When the dimension p is larger than the sample size n , it is challenging to develop statistical inference methods for high-dimensional measurement error regression models due to the existence of bias, nonconvexity of the objective function, high computational cost and many other difficulties. Over the past few years, some works have overcome the aforementioned difficulties and proposed several novel statistical inference methods. This paper mainly reviews the current development on estimation, hypothesis testing and variable screening methods for high-dimensional measurement error regression models and shows the theoretical results of these methods with some directions worthy of exploring in future research.

Keywords: convex optimization; estimation; high-dimensional data; hypothesis testing; measurement error; variable selection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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