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Nonparametric Homogeneity Pursuit in Functional-Coefficient Models

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Publication details

JournalJournal of Nonparametric Statistics
DateAccepted/In press - 28 Jun 2021
DateE-pub ahead of print (current) - 14 Jul 2021
Issue number3-4
Number of pages30
Pages (from-to)387-416
Early online date14/07/21
Original languageEnglish


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.

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

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