CONVERGENCY RATE OF MEAN INTEGRATED SQUARE ERROR IN DENSITY ESTIMATION BASED ON HERMITE POLYNOMIALS

CONVERGENCY RATE OF MEAN INTEGRATED SQUARE ERROR IN DENSITY ESTIMATION BASED ON HERMITE POLYNOMIALS

E. Er├želik

[PDF]

Abstract

The estimate of a probability density using a sequence X1;X2; :::;XN of independent and identically distributed (i.i.d) random variables with common unknown density function is studied by means of Hermite functions. We obtained convergency rate of the mean integrated square error (MISE) of density estimators by using delta sequences which are based on the hermite functions when the support of the density function is in nite. Then we obtained convergency rate of the mean square error (MSE) and MISE of estimator for the densities having compact support. The contribution of this work is improving the results of former publications about rate of convergence of estimators based on Hermite series.

Keywords

Delta Sequences; Rates of Convergence; Hermite Functions; Orthogonal Polynomials.