In statistical analysis, kernel density estimation is a widely used non-parametric method for estimating the probability density function (PDF) of a random variable. In this talk, I will discuss recent advances in the kernel estimation of the cumulative distribution function( CDF).

The first part of the talk will focus on IID (Independent and Identically Distributed) case, the law of the iterated logarithm (LIL) of L1-norms of kernel estimators for CDF. Then I shall extend the LIL to the Lp-norms of the residual-based kernel estimators of error CDF in AR(p) models. I will also consider the weak convergence of sequential kernel smoothed empirical process of the residuals in AR(p) models.

In the end, I shall show the unform strong consistency of residual-based kernel estimator of error CDF in the nonlinear autoregressive stationary time series model.

Fuxia Cheng is a Professor at the Department of Mathematics ,  Illinois State University. She holds a Master and a PhD degree in Statistics from Michigan State University (USA), a PhD degree in Applied Mathematics from Tsinghua University, a Master degree in Mathematics from Fudan University and a Bachelor in Mathematics from Shandong University. She has published papers in peer-reviewed journals such as Annals of Statistics, Journal of Multivariate Analysis, Sankhya A: the Indian Journal of Statistics, Journal of Nonparametric Statistics, Journal of Statistical Planning and Inference, Statistics & Probability Letters, Statistical Inference for Stochastic Processes, Communications in Statistics---Theory and Methods, Biometrics, Bioinformatics, Statistics, Metrika, etc. She has been on the editorial board of several journals.