Fast Plug-in Method for Parzen Probability Density Estimator Applied to Genetic Neutrality Study

In order to compute an optimal Kernel probability density function estimator (KDE), the plug-in method is considered in this paper. Such algorithm gives a way to optimize both the kernel and the bandwidth. Here, we propose a new procedure witch is faster than the common plug-in one. For each time, a factor J(f), which is linked to the second order derivative of the pdf, is analytically approximated. The pdf is estimated only once at the end of iterations. Different random variables with difficult distributions are generated in order to prove the efficiency of the proposed optimal estimator. These algorithms are then, applied to genetics data in order to give a better characterisation in the mean of neutrality of a given population by using the fast MISE optimal pdf estimation of the Tajima´s D criterion. This criterion is a statistic allowing the estimation of the genetic neutrality of the sample population.