Sensitivity analysis of partially linear models with response missing at random

ABSTRACT

This article investigates case-deletion influence analysis via Cook’s distance and local influence analysis via conformal normal curvature for partially linear models with response missing at random. Local influence approach is developed to assess the sensitivity of parameter and nonparametric estimators to various perturbations such as case-weight, response variable, explanatory variable, and parameter perturbations on the basis of semiparametric estimating equations, which are constructed using the inverse probability weighted approach, rather than likelihood function. Residual and generalized leverage are also defined. Simulation studies and a dataset taken from the AIDS Clinical Trials are used to illustrate the proposed methods.

KEYWORDS:

• Case-deletion influence analysis
• Generalized leverage
• Local influence analysis
• Missing at random
• Partially linear models

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G08
• 62H12
• 62J20

Acknowledgments

The authors are grateful to the editor, an associate editor, and two referees for their valuable suggestions and comments that greatly improved the manuscript.

Funding

The research was supported by grants from the National Science Fund for Distinguished Young Scholars of China (11225103).