Tail index varying coefficient model

ABSTRACT

This paper deals with a new class of tail index varying coefficient models with the random covariate under Pareto-type distributions. To estimate the unknown coefficient functions, we develop an estimation procedure via a local polynomial maximum likelihood techniques. The asymptotic normality of the estimated coefficient functions under some mild regularity conditions are established. Two numerical examples and one application are used to illustrate the performance of the proposed procedure.

KEYWORDS:

• Asymptotic normality
• Local polynomial fitting
• Pareto-type distributions
• Tail index
• Varying coefficient model.

AMS 2000 subject classification:

• 62G08
• 62G20
• 62G32

Acknowledgements

Research is supported by the Fundamental Research Funds for the Central Universities, the National Natural Science Foundation of China (Nos. 11371318 and 11731012), Zhejiang Provincial Natural Science Foundation (Nos. LY17A010016 and LY18A010005) and Funding Project for First-Class Discipline (Mathematics) Construction in Higher Education of Ningxia. The authors are very grateful to the anonymous referee, the editor and the associate editor for their constructive and helpful comments.

Additional information

Funding

Natural Science Foundation of Zhejiang Province (LY17A010016/ LY18A010005) the National Natural Science Foundation of China (11371318/11731012) the Fundamental Research Funds for the Central Universities (2016QNA3001)