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Optimal two-stage procedures for estimating location and size of the maximum of a multivariate regression function

2012
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Annals of Statistics
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We propose a two-stage procedure for estimating the location $\bolds{\mu}$ and size M of the maximum of a smooth d-variate regression function f. In the first stage, a preliminary estimator of $\bolds{\mu}$ obtained from a standard nonparametric smoothing method is used. At the second stage, we "zoom-in" near the vicinity of the preliminary estimator and make further observations at some design points in that vicinity. We fit an appropriate polynomial regression model to estimate the location

doi:10.1214/12-aos1053
fatcat:66l4t57gx5fdfberudx25x2qle