The T-type estimate of a class of partially non linear models

Abstract

This paper considers a partially non linear model E(Y|X, z, t) = f(X, β) + z^Tg(t) and gives its T-type estimate, which is a weighted quasi-likelihood estimate using sieve method and can be obtained by EM algorithm. The influence functions and asymptotic properties of T-type estimate (consistency and asymptotic normality) are discussed, and convergence rate of both parametric and non parametric components are obtained. Simulation results show the shape of influence functions and prove that the T-type estimate performs quite well. The proposed estimate is also applied to a data set and compared with the least square estimate and least absolute deviation estimate.

KEYWORDS:

• T-type
• Partially non linear
• Influential function
• Consistency
• Convergence rate

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G35, 62G08, 62J02

Acknowledgment

The authors express their gratitude to the editor and the referees whose comments greatly improved this paper.

Funding

The research of Hengjian Cui was supported by the Natural Science Foundation of China (Nos. 11071022, 11028103, 11471223, and 11231010), the Key project of Beijing Municipal Educational Commission (KZ201410028030) and the Foundation of Beijing Center of Mathematics and Informatics. The research of Tao Hu was supported by the Natural Science Foundation of China (11201317), the Beijing Municipal Education Commission Foundation (KM201210028005), and the Doctoral Fund of Ministry of Education of China (20111108120002). The research of Lele Huang was supported by the Natural Science Foundation of China (No. 71031001).