程福霞教授学术报告：Asymptotics of Distribution Estimation in Linear Autoregressive Models
报告题目： Asymptotics of Distribution Estimation in Linear AutoregressiveModels
报 告 人： Prof. Fuxia Cheng (Department of Mathematics, Illinois StateUniversity)
For thelinear autoregressive stationary time series model, I consider estimation ofthe error distribution, including density and cumulative distribution (CDF)functions, and error variance.
For thedistribution of the error density estimator, at a fixed point, is shown to benormal. Globally, the asymptotic distribution of the maximum of a suitablynormalized deviation of the density estimator from the expectation of thekernel error density (based on the true error) is the same as in the case ofthe one sample set up, which is given in Bickel and Rosenblatt (1973). Theclassical Glivenko-Cantelli Theorem is extended to the residual based kernelsmooth CDF estimator in the autoregressive model. The asymptotic distributionof the error variance estimator is shown to be normal. And we also obtain thestrong consistency of the proposed error variance estimator.