报告题目： Kernel entropy estimation for linear processes
报告人：Hailin Sang University of Mississippi
报告时间：6月4日 16:00-17:00
地点：1518
摘要：
Entropy is widely applied in the fields of information theory, statistical classification, pattern recognition and so on since it is a measure of uncertainty in a probability distribution. The quadratic functional plays an important role in the study of quadratic R/'{e}nyi entropy and the Shannon entropy.
It is a challenging problem to study the estimation of the quadratic functional and the corresponding entropies for dependent case.
In this talk, we consider the estimation of the quadratic functional for linear processes. With a Fourier transform on the kernel function and the projection method, it is shown that, the kernel estimator has similar asymptotical properties as the i.i.d. case studied in Gin/'{e} and Nickl (2008) if the linear process $/{X_n: n/in /N/}$ has the defined short range dependence. We also provide an application to $L^2_2$ divergence and the extension to multivariate linear processes. The simulation study for linear processes with Gaussian and $/alpha$-stable innovations confirms the theoretical results. As an illustration, we estimate the $L^2_2$ divergences among the density functions of average annual river flows for four rivers and obtain promising results.