Improved statistical inference on semiparametric varying-coefficient partially linear measurement error model

ABSTRACT

In this paper, we consider the estimation and goodness-of-fit test of a semiparametric varying-coefficient partially linear (SVCPL) model when both responses and part of covariates are measured with error. It is assumed that the true variables are measurable functions of some auxiliary variables. The often-used assumptions on the measurement error, such as a known error variance, a known distribution of the error variable, a validation sample or a repeated data set, are not required. The asymptotic properties of the proposed estimators and testing statistic are investigated. We show that the application of the measurement error structures can improve the efficiency of estimating and testing methods. The performances of the estimating and testing methods are illustrated by simulation studies and an application to a real data set.

KEYWORDS:

• measurement error
• model adjustment
• profile likelihood
• empirical process
• model check

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62G05
• 62G10

Acknowledgements

The authors would like to thank the Associate Editor and two reviewers for their careful review and insightful comments that have led to significant improvement of this article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11571340) and the Open Project of Key Laboratory of Big Data Mining and Knowledge Management, CAS.