Nonparametric homogeneity pursuit in functional-coefficient models

ABSTRACT

This paper explores the homogeneity of coefficient functions in nonlinear models with functional coefficients and identifies the underlying semiparametric modelling structure. With initial kernel estimates, we combine the classic hierarchical clustering method with a generalised version of the information criterion to estimate the number of clusters, each of which has a common functional coefficient, and determine the membership of each cluster. To identify a possible semi-varying coefficient modelling framework, we further introduce a penalised local least squares method to determine zero coefficients, non-zero constant coefficients and functional coefficients which vary with an index variable. Through the nonparametric kernel-based cluster analysis and the penalised approach, we can substantially reduce the number of unknown parametric and nonparametric components in the models, thereby achieving the aim of dimension reduction. Under some regularity conditions, we establish the asymptotic properties for the proposed methods including the consistency of the homogeneity pursuit. Numerical studies, including Monte-Carlo experiments and two empirical applications, are given to demonstrate the finite-sample performance of our methods.

KEYWORDS:

• Functional-coefficient models
• homogeneity
• information criterion
• nonparametric estimation
• penalised method

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62G05
• 62G20

Acknowledgments

The authors thank the Editor-in-Chief, an Associate Editor and two reviewers for their valuable comments, which improve the former version of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Chen's research was partially supported by Grant 65617357 from the Economic and Social Research Council of the United Kingdom.