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Biometrika 1972 59(2):387-394; doi:10.1093/biomet/59.2.387
© 1972 by Biometrika Trust
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The distribution of the maximum likelihood estimator of the parameter in the first-order autoregressive series

J. E. REEVES

University College of Wales Aberystwyth

A method is given for obtaining values of the distribution function of the maximum likelihood estimator of the parameter in the first-order autoregressive series. Although exact results are obtainable in a special case, in general the distribution function involves the approximation of the distribution of a linear combination of chi-squared variates. Two such approximations are compared with simulated results. The method used is valid for any value of the parameter.

Key Words: First-order autoregressive series • Distribution of serial correlation coefficient • Linear combinations of chi-squared variates


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