Adaptive estimation in symmetric location model under log-concavity constraint
Abstract
We revisit the problem of estimating the center of symmetry of an unknown symmetric density . Although stone (1975), Eden (1970), and Sacks (1975) constructed adaptive estimators of in this model, their estimators depend on external tuning parameters. In an effort to reduce the burden of tuning parameters, we impose an additional restriction of log-concavity on . We construct truncated one-step estimators which are adaptive under the log-concavity assumption. Our simulations suggest that the untruncated version of the one step estimator, which is tuning parameter free, is also asymptotically efficient. We also study the maximum likelihood estimator (MLE) of in the shape-restricted model.
Cite
@article{arxiv.2105.04287,
title = {Adaptive estimation in symmetric location model under log-concavity constraint},
author = {Nilanjana Laha},
journal= {arXiv preprint arXiv:2105.04287},
year = {2023}
}
Comments
In this version, several minor mistakes in the previous version have been corrected. You can find a detailed list of these corrections on the last page of this manuscript. To summarize, fixed algebraic mistake in Theorem 1 proof. Corrected (log n)^2 to (log n)^4 in Lemma B.12. Revised proof of Fact 4 using algebraic inequality (Fact 16)