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Báo cáo hóa học: " Research Article Analytical Plug-In Method for Kernel Density Estimator Applied to Genetic Neutrality Study"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Analytical Plug-In Method for Kernel Density Estimator Applied to Genetic Neutrality Study | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2008 Article ID 739082 8 pages doi 10.1155 2008 739082 Research Article Analytical Plug-In Method for Kernel Density Estimator Applied to Genetic Neutrality Study Molka Troudi 1 2 Adel M. Alimi 1 and Samir Saoudi2 1 REGIM Ecole Nationale des Ingenieurs de Sfax Route de Soukra Km 1.5 3002 Sfax Tunisia 2 Departement Signal et Communications TELECOM Bretagne Institut TELECOM Technopole Brest-Iroise CS 83818 29283 Brest Cedex 3 France Correspondence should be addressed to Samir Saoudi samir.saoudi@enst-bretagne.fr Received 21 November 2007 Accepted 1 May 2008 Recommended by Jar-Ferr Yang The plug-in method enables optimization of the bandwidth of the kernel density estimator in order to estimate probability density functions pdfs . Here a faster procedure than that of the common plug-in method is proposed. The mean integrated square error MISE depends directly upon J f which is linked to the second-order derivative of the pdf. As we intend to introduce an analytical approximation of J f the pdf is estimated only once at the end of iterations. These two kinds of algorithm are tested on different random variables having distributions known for their difficult estimation. Finally they are applied to genetic data in order to provide a better characterisation in the mean of neutrality of Tunisian Berber populations. Copyright 2008 Molka Troudi et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. INTRODUCTION The problem of estimation of a probability density function f x is interesting for many reasons among which are the possible applications in the field of discriminant analysis or the estimation of functions of the density. The parametric approach to density estimation assumes a functional form for the density and then .