Convergence Rate of the Best-r-Points-Average Estimator the Maximizer of a Multivariate Regression Function

BRPA estimator, proposed in Changchien (1990), 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, Huang and Huang (1996), Bai and Huang (1999), Wu and Wang (2000) and Bai, Chen and Wu (2003). In this article, we give the convergence rate of the BRPA estimator of the multivariate regression function under some mild conditions and popularize the result of Bai, Chen and Wu (2003).