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Convergence rate of the best-r-point-average estimator for the maximizer of a nonparametric regression function

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  • Bai, Zhidong
  • Chen, Zehua
  • Wu, Yaohua

Abstract

The best-r-point-average (BRPA) estimator of the maximizer of a regression function, proposed in Changchien (in: M.T. Chao, P.E. Cheng (Eds.), Proceedings of the 1990 Taipei Symposium in Statistics, June 28-30, 1990, pp. 63-78) has certain merits over the estimators derived through the estimation of the regression function. Some of the properties of the BRPA estimator have been studied in Chen et al. (J. Multivariate Anal. 57 (1996) 191) and Bai and Huang (Sankhya: Indian J. Statist. Ser. A. 61 (Pt. 2) (1999) 208-217). In this article, we further study the properties of the BRPA estimator and give its convergence rate under some quite general conditions. Simulation results are presented for the illustration of the convergence rate. Some comparisons with existing estimators such as the Müller estimator are provided.

Suggested Citation

  • Bai, Zhidong & Chen, Zehua & Wu, Yaohua, 2003. "Convergence rate of the best-r-point-average estimator for the maximizer of a nonparametric regression function," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 319-334, February.
    • Handle: RePEc:eee:jmvana:v:84:y:2003:i:2:p:319-334
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    References listed on IDEAS

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    1. Chen, Hung & Huang, Mong-Na Lo & Huang, Wen-Jang, 1996. "Estimation of the Location of the Maximum of a Regression Function Using Extreme Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 191-214, May.
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    Cited by:

    1. Burman, Prabir & Polonik, Wolfgang, 2009. "Multivariate mode hunting: Data analytic tools with measures of significance," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1198-1218, July.

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