Influence Diagnostics of Semiparametric Nonlinear Reproductive Dispersion Models

Abstract

This article proposes a semiparametric nonlinear reproductive dispersion model (SNRDM) which is an extension of nonlinear reproductive dispersion model and semiparametric regression model. Maximum penalized likelihood estimators (MPLEs) of unknown parameters and nonparametric functions in SNRDMs are presented. Some novel diagnostic statistics such as Cook distance and difference deviance for parametric and nonparametric parts are developed to identify influence observations in SNRDMs on the basis of case-deletion method, and some formulae readily computed with the MPLEs algorithm for diagnostic measures are given. The equivalency of case-deletion models and mean-shift outlier models in SNRDM is investigated. A simulation study and a real example are used to illustrate the proposed diagnostic measures.

Keywords:

• Case deletion models
• Influence diagnostics
• Maximum penalized likelihood estimators
• Mean-shift outlier models
• Semiparametric nonlinear reproductive dispersion models

Mathematics Subject Classification:

• 62J02
• 62J20

Acknowledgments

The authors are grateful to Editor and a referee for constructive suggestions that greatly improved the article. This work was partially supported by the National Natural Science Foundation of China (10960126, 10761011), ZJNSF (Y606667), the Ph.D. Special Scientific Research Foundation of Chinese University (20060673002), and by the program for New Century Excellent Talents in University (NCET-07-0737) and Middle-aged & Young Professionals and Academic Leaders of Yunnan Province.