The optimal wavelet estimation for biased density

Junlian Xu

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 24, 8728-8740

Abstract: In this paper, the optimal estimation at a given point is considered for biased density in theory. A lower bound is first provided for all possible estimators over the local Hölder space. Using wavelet method, a linear wavelet estimator is constructed and turned out to be optimal by investigating its upper bound of pointwise convergence rate. To get the adaptivity, a nonlinear wavelet estimator is obtained and proved to be near-optimal within a logarithmic factor.

Date: 2022
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DOI: 10.1080/03610926.2021.1905845

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