publication . Article . Other literature type . 1997

Optimal smoothing in adaptive location estimation

Byeong U. Park; Enno Mammen;
Open Access English
  • Published: 15 Mar 1997
  • Publisher: North-Holland Publ. Co.
  • Country: Germany
Abstract
In this paper, we consider higher order performance of kernel based adaptive location estimates. We show how much one loses in efficiency without knowing the underlying translation density, and derive the optimal order of the bandwidths involved in kernel estimation of the efficient score function. The optimal order is obtained by minimizing the loss of efficiency in terms of estimating the location parameter. The main lesson here is that the optimal order of the bandwidths are different from those for optimal estimation of the score function. This implies that optimal estimation of the score function does not lead to second order optimal location estimation.
Subjects
free text keywords: 310, 310 General statistics, 510, 510 Mathematics, Statistics, Probability and Uncertainty, Statistics and Probability, Applied Mathematics, Location parameter, Kernel density estimation, Kernel (linear algebra), Mathematics, Mathematical optimization, Smoothing, Score, Optimal estimation, Variable kernel density estimation
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