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Nonparametric homogeneity pursuit in functional-coefficient models

Author

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  • Jia Chen
  • Degui Li
  • Lingling Wei
  • Wenyang Zhang

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.

Suggested Citation

  • Jia Chen & Degui Li & Lingling Wei & Wenyang Zhang, 2021. "Nonparametric homogeneity pursuit in functional-coefficient models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 33(3-4), pages 387-416, October.
    • Handle: RePEc:taf:gnstxx:v:33:y:2021:i:3-4:p:387-416
    DOI: 10.1080/10485252.2021.1951265
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    References listed on IDEAS

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    1. Wang, Hansheng & Xia, Yingcun, 2009. "Shrinkage Estimation of the Varying Coefficient Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 747-757.
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    Cited by:

    1. Xiaorong Yang & Jia Chen & Degui Li & Runze Li, 2023. "Functional-Coefficient Quantile Regression for Panel Data with Latent Group Structure," Papers 2303.13218, arXiv.org.

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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