Nonparametric Homogeneity Pursuit in Functional-Coefficient Models

TY - JOUR

T1 - Nonparametric Homogeneity Pursuit in Functional-Coefficient Models

AU - Chen, Jia

AU - Li, Degui

AU - Wei, Lingling

AU - Zhang, Wenyang

N1 - © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group

PY - 2021/7/14

Y1 - 2021/7/14

N2 - This paper explores 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.

AB - This paper explores 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.

U2 - 10.1080/10485252.2021.1951265

DO - 10.1080/10485252.2021.1951265

M3 - Article

SN - 1048-5252

VL - 33

SP - 387

EP - 416

JO - Journal of Nonparametric Statistics

JF - Journal of Nonparametric Statistics

IS - 3-4

ER -