The Research On Asymptotic Property Of The Entropy Functional Estimation Under Dependent Samples

Let {X_i ,i≥1}be a stochastic sequence. The entropy function is defined as ,x∈Rdbased on samples X₁ , X₂,…,X_n with a common unknown probability density function f ( x).So Many experts always are interested in how to construct the estimation of entropy function and study its statistical property. This paper introduces the estimation of entropy function and asymptotic property under i.i.d. andφ-mixing samples. And on this basis, constructs the entropy function H ( f )of histogram estimation underα-mixing samples X₁ , X₂,…,X_n,Xnusing the Bernstein inequality, obtains the strong consistency of estimation under certain conditions, extends the results of the present literature.