Statistical Inference for Semiparametric Varying-coefficient Partially Linear Models with Generated Regressors...

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Semiparametric varying-coefficient partially linear models are widely used but face challenges with unobserved covariates.
• Existing methods often struggle when only ancillary variables are available for error-prone covariates.

Purpose of the Study:

• To develop robust estimation procedures for parametric and nonparametric components in the presence of unobserved covariates.
• To introduce novel statistical tests for identifying significant components within these models.
• To enhance the accuracy of hypothesis testing for small or moderate sample sizes.

Main Methods:

• Developed semiparametric profile least-square-based estimation procedures.
• Calibrated error-prone covariates using ancillary variables.
• Proposed profile least-square-based ratio test and Wald test.
• Introduced a Wild bootstrap version for improved test accuracy.

Main Results:

• Established asymptotic properties of the proposed estimators.
• Demonstrated the effectiveness of the proposed estimation and testing procedures through simulation experiments.
• The Wild bootstrap method enhances test accuracy for smaller datasets.

Conclusions:

• The proposed semiparametric profile least-square-based methods provide a reliable framework for analyzing models with unobserved covariates.
• The developed tests, including the Wild bootstrap version, offer accurate tools for component significance identification.
• This research contributes valuable statistical techniques for handling complex data structures in various scientific fields.