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arXiv · 1411.0515

Efficient pointwise estimation based on discrete data in ergodic nonparametric diffusions

L. I. Galtchouk·S. M. Pergamenshchikov
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Abstract

A truncated sequential procedure is constructed for estimating the drift coefficient at a given state point based on discrete data of ergodic diffusion process. A nonasymptotic upper bound is obtained for a pointwise absolute error risk. The optimal convergence rate and a sharp constant in the bounds are found for the asymptotic pointwise minimax risk. As a consequence, the efficiency is obtained of the proposed sequential procedure.

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L. I. Galtchouk, S. M. Pergamenshchikov. 2015-09-18. Efficient pointwise estimation based on discrete data in ergodic nonparametric diffusions. https://doi.org/10.3150/14-bej655

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