Numerical results concerning a sharp adaptive density estimator
type: Item
instance of: scholarly article
title: Numerical results concerning a sharp adaptive density estimator
zbMATH Open document ID: 1007.62026
author: Cristina Butucea
published in: Computational Statistics
publication date: 2003-03-09T00:00:00Z
full work available at URL: http://edoc.hu-berlin.de/18452/3905
review text: A local adaptive kernel density estimator is described for densities \(f\) with \(\int(f^{(\beta)})^2dx\leq L^2\), where \(f^{(\beta)}\) is the derivative, may be fractional, and \(L\) is supposed to be fixed and known. A specific procedure for estimation of \(\beta\) is considered. The adaptive procedure is based on a pilot estimator \(f_n\). The adaptive bandwidth is \[ h_{n,\beta}(x)=[(\max(f_n(x),1/\ln n)\cdot\ln n)/n\beta(2\beta-1)L^2]^{1/(2\beta)}, \] and the kernel used in the final estimator is \[ K_\beta(x)=\pi^{-1}\int_0^\infty(1+|u|^{2\beta})^{-1}\cos(xu)du. \] The final locally adaptive estimator is \[ (nh_{n,\beta}(x))^{-1}\sum_{j=1}^n K_\beta\left((X_j-x)/h_{n,\beta}(x)\right), \] where \((X_1,\dots,X_n)\) is an i.i.d. sample. Simulation results are presented for some distributions.
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62-08
zbMATH DE Number: 1878613
zbMATH Keywords: bandwidth selection
zbMATH Keywords: local adaptive estimation
zbMATH Keywords: Lepski criterion
MaRDI profile type: Publication
OpenAlex ID: W1996337892
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DOI: 10.1007/S001800100065
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description: scientific article; zbMATH DE number 1878613