Saddlepoint Approximation for the Least Squares Estimation in First-Order Autoregression
2018
Lieberman, Offer
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.
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