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

  • Authors:

  • Zhidong Bai;Zehua Chen;Yaohua Wu

  • Affiliations:

  • Department of Mathematics, North East Normal University, Jilin 130024, China and Department of Statistics and Applied Probability, National University of Singapore, Singapore 119260, Singapore;Department of Statistics and Applied Probability, National University of Singapore, Singapore 119260, Singapore;Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2003

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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.