Estimation and inference for generalized semi-varying coefficient models

ABSTRACT

This paper is concerned with the estimation and inference in generalized semi-varying coefficient models. An orthogonal projection local quasi-likelihood estimation is investigated, which can easily be used to estimate the model parametric and nonparametric parts. Then an empirical likelihood logarithmic approach to construct the confidence regions/intervals of the nonparametric parts is developed. Under some mild conditions, the asymptotic properties of the resulting estimators are studied explicitly, respectively. Some simulation studies are carried out to examine the finite sample performance of the proposed methods. Finally, the methodologies are illustrated by a real data set.

KEYWORDS:

• Generalized semi-varying coefficient models
• orthogonal projection
• empirical likelihood
• confidence regions

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [Grant Nos. 11701286, 11571073], the Natural Science Foundation of Jiangsu Province of China [Grant No. BK20171073], the Natural Science Foundation of the Jiangsu Higher Education Institutions of China [Grant No. 17KJB110006], and the Philosophy and Social Science Foundation of the Jiangsu Higher Education Institutions of China [Grant No. 2017SJB0350].