ON DENSITY ESTIMATION
Abstract
Let R(,L(,1))(f(,n),f), R(,K)(f(,n),f) be the risks of the density estimator f(,n) of(' ) the density function f under mean deviation and square of Kakutani distance respectively. Sufficient conditions are given so that R(,L(,1))(f(,n),f) and R(,K)(f(,n),f) of kernel estimators and histogram(' ) estimators go to 0 as the sample size n tends to infinity. Lower bounds of convergence rates of R(,L(,1))(f(,n),f) and R(,K)(f(,n),f) of kernel(' ) estimator are obtained. The exact convergence rates of R(,L(,1))(f(,n),f)(' ) for inverse flat window estimators are obtained under appropriate smoothness conditions. Besides, a method that facilitates computations is obtained for constructing the prior distribution over the set of density functions. Also, a method of drawing a random sample from a randomly chosen density is indicated.
Degree
Ph.D.
Subject Area
Statistics
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