Almost sure convergence of estimator for the entropy function based on α-mixing samples
Zhong-han Li · Journal of Hefei University of Technology · 2008
Let{Xi,i≥1}be α-mixing stochastic sequence with a common unknown probability density function f(x).The Shannon entropy is defined as H(f)=-integral from n=-∞ to ∞ (f(x)logf(x)dx),x∈Rd.The paper investigates almost sure convergence of histogram estimation Hn=-∫fn(x)≥anfn(x)logfn(x)dx for H(f) based on a random sample X1,X2,…,Xn under certain conditions.The results of the present literature are extended.