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Local rank estimation and related test for varying-coefficient partially linear models

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  • Jing Sun
  • Lu Lin

Abstract

This paper develops a robust estimation procedure for the varying-coefficient partially linear model via local rank technique. The new procedure provides a highly efficient and robust alternative to the local linear least-squares method. In other words, the proposed method is highly efficient across a wide class of non-normal error distributions and it only loses a small amount of efficiency for normal error. Moreover, a test for the hypothesis of constancy for the nonparametric component is proposed. The test statistic is simple and thus the test procedure can be easily implemented. We conduct Monte Carlo simulation to examine the finite sample performance of the proposed procedures and apply them to analyse the environment data set. Both the theoretical and the numerical results demonstrate that the performance of our approach is at least comparable to those existing competitors.

Suggested Citation

  • Jing Sun & Lu Lin, 2014. "Local rank estimation and related test for varying-coefficient partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 187-206, March.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:1:p:187-206
    DOI: 10.1080/10485252.2013.841910
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    References listed on IDEAS

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    1. Shang, Suoping & Zou, Changliang & Wang, Zhaojun, 2012. "Local Walsh-average regression for semiparametric varying-coefficient models," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1815-1822.
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    Cited by:

    1. Zhaoliang Wang & Liugen Xue & Gaorong Li & Fei Lu, 2019. "Spline estimator for ultra-high dimensional partially linear varying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 657-677, June.
    2. Jing Yang & Hu Yang & Fang Lu, 2019. "Rank-based shrinkage estimation for identification in semiparametric additive models," Statistical Papers, Springer, vol. 60(4), pages 1255-1281, August.

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