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On nonparametric estimators of location of maximum. (English) Zbl 1356.62048

Summary: An estimator of the maximum of a regression function and its location is often of greater interest than an estimator of the regression curve itself. We review properties of nonparametric estimators of the location of maximum and investigate the influence of the density of design points on the asymptotic distribution of the estimator. Classical calculus of variations is used to find the optimal distribution of the design points for the nonparametric kernel estimator of the location of maximum.

MSC:

62G05 Nonparametric estimation
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