Nonparametric Homogeneity Pursuit in Functional-Coefficient Models

Jia Chen, Degui Li, Lingling Wei and Wenyang Zhang

Discussion Papers from Department of Economics, University of York

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 of coefficient functions, 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 an empirical application, are given to demonstrate the finite-sample performance of our methods.

Keywords: Functional-coefficient models; Hierarchical agglomerative clustering; Homogeneity; Information criterion; Nonparametric estimation; Penalised method (search for similar items in EconPapers)
JEL-codes: C13 C14 (search for similar items in EconPapers)
Date: 2019-03
New Economics Papers: this item is included in nep-ecm and nep-ore
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Journal Article: Nonparametric homogeneity pursuit in functional-coefficient models (2021)
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