Séminaire Mathématique de Béjaia
Volume 11, Numéro 1, Pages 77-78
2012-12-31
On The Estimation Of The Mode By Orthogonal Series
Authors : Saadi Nora . Adjabi Smail .
Abstract
The simplicity and good performance of orthogonal series density estimator have found favor with several authors, and have been applied to several different areas (harmonic analysis, signal processing, image compression, physical analysis, functional statistics ...). This paper addresses the problem of estimating the mode of a density function under non parametric conditions based on an orthogonal series. We give a rigorous, theoretical account of the estimator’s properties(bias, variance, mean square error, convergence of the bias, convergence of the variance, convergence of the mean square error and convergence in probability). Our results show that some of the theoretical properties of Orthogonal series’s estimator are similar to those of Parzen’s estimator. For example, under the condition that the density has two bounded derivatives in a neighborhood of the mode, and the density is uniformly continuous.
Keywords
Mode estimation, Orthogonal series,Density estimation, Convergence in probability.
Les articles similaires
بوسالم أحلام
.
عابد يوسف
.
ص 117-132.
Yahia Zeghoudi
.
pages 74-88.
Said Houari Amel
.
pages 257-268.
Nezli Lazhari
.
Zouaid Omar
.
pages 59-68.
