Discussiones Mathematicae Probability and Statistics 22(1,2) (2002) 15-26

APPROXIMATE BIAS FOR FIRST-ORDER AUTOREGRESSIVE MODEL WITH UNIFORM INNOVATIONS. SMALL SAMPLE CASE

Karima Nouali and Hocine Fellag

 Department of Mathematics
Faculty of Sciences, University of Tizi-Ouzou
Tizi-Ouzou, 15000 Algeria
e-mail: k-nouali@hotmail.com
e-mail: hfellag@yahoo.com

Abstract

The first-order autoregressive model with uniform innovations is considered. The approximate bias of the maximum likelihood estimator (MLE) of the parameter is obtained. Also, a formula for the approximate bias is given when a single outlier occurs at a specified time with a known amplitude. Simulation procedures confirm that our formulas are suitable. A small sample case is considered only.

Keywords: autoregressive model, bias, outlier, uniform distribution.

2000 Mathematics Subject Classification: 62F11, 62M10.

References

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Y.J. Choi, Kolmogorov-Smirnov Test with Nuisance Parameters in Uniform Case, M.S. Thesis, University of Washington 1980. 
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A.J. Fox, Outliers in time series, J. Roy. Stat. Soc. 34 (B) (1972), 350-363.

Received 15 March 2002