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Asymptotic normality of Powell’s kernel estimator

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Abstract

We establish asymptotic normality of Powell’s kernel estimator for the asymptotic covariance matrix of the quantile regression estimator for both i.i.d. and weakly dependent data. As an application, we derive the optimal bandwidth that minimizes the approximate mean squared error of the kernel estimator. We also derive the corresponding results to censored quantile regression.

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Authors and Affiliations

  1. Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima, 739-8526, Japan

    Kengo Kato

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  1. Kengo Kato
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Correspondence to Kengo Kato.

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Kato, K. Asymptotic normality of Powell’s kernel estimator. Ann Inst Stat Math 64, 255–273 (2012). https://doi.org/10.1007/s10463-010-0310-9

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  • DOI: https://doi.org/10.1007/s10463-010-0310-9

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