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 ofKakutani distance respectively. Sufficient conditions are given sothat 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. Lowerbounds 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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