β Scribed by Enno Mammen; Byeong U. Park
No coin nor oath required. For personal study only.
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.
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