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Model detection and estimation for single-index varying coefficient model

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  • Feng, Sanying
  • Xue, Liugen

Abstract

Single-index varying coefficient model (SIVCM) is a powerful tool for modeling nonlinearity in multivariate estimation, and has been widely used in the literature due to the fact that it can overcome the well-known phenomenon of “curse-of-dimensionality”. In this paper, we consider the problem of model detection and estimation for SIVCM. Based on the proposed combined penalization procedure, we can identify the true model structure consistently, and obtain a new semiparametric model—partially linear single-index varying coefficient model (PLSIVCM). Under the appropriate conditions, we demonstrate that the proposed penalized estimators of parametric and nonparametric components of PLSIVCM are consistent, but their asymptotic distributions are not available. Hence, we extend the minimum average variance estimation method to PLSIVCM, and establish the asymptotic normality for the refined estimators of index parameters, constant coefficients and varying coefficient functions, respectively. The finite sample performances of the proposed methods are illustrated by a Monte Carlo simulation study and the real data analysis.

Suggested Citation

  • Feng, Sanying & Xue, Liugen, 2015. "Model detection and estimation for single-index varying coefficient model," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 227-244.
    • Handle: RePEc:eee:jmvana:v:139:y:2015:i:c:p:227-244
    DOI: 10.1016/j.jmva.2015.03.008
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    Cited by:

    1. Peng Lai & Fangjian Wang & Tingyu Zhu & Qingzhao Zhang, 2021. "Model identification and selection for single-index varying-coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 457-480, June.
    2. Chaohui Guo & Hu Yang & Jing Lv, 2018. "Two step estimations for a single-index varying-coefficient model with longitudinal data," Statistical Papers, Springer, vol. 59(3), pages 957-983, September.
    3. Jun Zhang & Junpeng Zhu & Zhenghui Feng, 2019. "Estimation and hypothesis test for single-index multiplicative models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 242-268, March.
    4. Lai, Peng & Zhang, Qingzhao & Lian, Heng & Wang, Qihua, 2016. "Efficient estimation for the heteroscedastic single-index varying coefficient models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 84-93.

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