Sankhya: The Indian Journal of Statistics

2005, Volume 67, Pt. 3, 553--567

Asymptotic Distributions of Error Density Estimators in First-order  Autoregressive Models

Fuxia Cheng, Illinois State University, Normal, USA

SUMMARY. This paper considers the asymptotic distributions of the error density estimators in   first-order autoregressive models.  At  a fixed point,  the distribution of  the error density estimator is shown to be normal. Globally,  the asymptotic distribution of the maximum of a suitably normalized deviation of the density estimator from the expectation of  the kernel error density (based on the true error) is the same as in the case of the one sample set up, which is given in Bickel and Rosenblatt (1973).

AMS (1991) subject classification. Primary 62G07; secondary 62M10.

Key words and phrases. AR(1) process, residuals, kernel density estimation.

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