Asymptotics for Kernel estimators of CDF in Autoregressive Models

Music City Center 

In this talk, I will discuss recent advances in the strong convergence of the kernel estimation of the cumulative distribution function (CDF). The first part of the talk focuses on the law of the iterated logarithm (LIL) of L1-norms of kernel estimators for CDF based on the independent and identically distributed (i.i.d) data. The second part extends the LIL of i.i.d case to that of Lp-norms of the residual-based kernel estimators of error CDF in the Autoregressive Models. Some simulation results showing the estimators' performances.

Kernel Estimator

Autoregressive Models

Lp-norm

LIL 

Section on Nonparametric Statistics