Saddlepoint Approximation for the Least Squares Estimation in First-Order Autoregression

In an earlier article, Phillips (1978) extended Daniels' (1956) approximation to the density of a modified correlation coefficient to obtain a saddlepoint approximation to the density of the least squares estimator in the first order non-circular autoregression. It was demonstrated that the resulting approximation is undefined in a substantial part of the tails. In this note, we establish that a suitable deformation of the contour of integration leads to a different type of saddlepoint approximation which is defined everywhere on the support of the density. It is further shown that the relative error of this approximation is bounded in the extreme tails.


Issue Date:
Jul 01 1994
Publication Type:
Working or Discussion Paper
Record Identifier:
http://ageconsearch.umn.edu/record/267631
Language:
English
Total Pages:
13
Series Statement:
Working Paper No. 14/94




 Record created 2018-02-01, last modified 2018-02-02

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