# Asymptotic normality of the integrated square error of a density estimator in the convolution model.

SORT (2004)

- Volume: 28, Issue: 1, page 9-26
- ISSN: 1696-2281

## Access Full Article

top## Abstract

top## How to cite

topButucea, Cristina. "Asymptotic normality of the integrated square error of a density estimator in the convolution model.." SORT 28.1 (2004): 9-26. <http://eudml.org/doc/40449>.

@article{Butucea2004,

abstract = {In this paper we consider a kernel estimator of a density in a convolution model and give a central limit theorem for its integrated square error (ISE). The kernel estimator is rather classical in minimax theory when the underlying density is recovered from noisy observations. The kernel is fixed and depends heavily on the distribution of the noise, supposed entirely known. The bandwidth is not fixed, the results hold for any sequence of bandwidths decreasing to 0. In particular the central limit theorem holds for the bandwidth minimizing the mean integrated square error (MISE). Rates of convergence are sensibly different in the case of regular noise and of super-regular noise. The smoothness of the underlying unknown density is relevant for the evaluation of the MISE.},

author = {Butucea, Cristina},

journal = {SORT},

keywords = {Inferencia no paramétrica; Estimación; Función densidad de probabilidad; Convolución; Comportamiento asintótico; Teorema central del límite; convolution density estimation; nonparametric density estimation; central limit theorem; integrated squared error; noisy observations},

language = {eng},

number = {1},

pages = {9-26},

title = {Asymptotic normality of the integrated square error of a density estimator in the convolution model.},

url = {http://eudml.org/doc/40449},

volume = {28},

year = {2004},

}

TY - JOUR

AU - Butucea, Cristina

TI - Asymptotic normality of the integrated square error of a density estimator in the convolution model.

JO - SORT

PY - 2004

VL - 28

IS - 1

SP - 9

EP - 26

AB - In this paper we consider a kernel estimator of a density in a convolution model and give a central limit theorem for its integrated square error (ISE). The kernel estimator is rather classical in minimax theory when the underlying density is recovered from noisy observations. The kernel is fixed and depends heavily on the distribution of the noise, supposed entirely known. The bandwidth is not fixed, the results hold for any sequence of bandwidths decreasing to 0. In particular the central limit theorem holds for the bandwidth minimizing the mean integrated square error (MISE). Rates of convergence are sensibly different in the case of regular noise and of super-regular noise. The smoothness of the underlying unknown density is relevant for the evaluation of the MISE.

LA - eng

KW - Inferencia no paramétrica; Estimación; Función densidad de probabilidad; Convolución; Comportamiento asintótico; Teorema central del límite; convolution density estimation; nonparametric density estimation; central limit theorem; integrated squared error; noisy observations

UR - http://eudml.org/doc/40449

ER -