Abstract
This paper deals with the density for a class of estimators _??_c1 c2 (c1, c2≥0) in Gaussian AR (1) process. Here _??_c1 c2 includes various estimators if the constants c1 and c2 are specified appropriately. Applying the saddlepoint method to the general formula by Geary [5], the density of _??_c1 c2 is approximated. Although Phillips [14] pointed out that the saddlepoint density is undefined in a substantial part of the tails, we elucidate that the resulting approximation is always defined if c1 and c2 are appropriately chosen. Some numerical comparisons are made among the Edgeworth approximation, the saddlepoint approximation, and the exact distribution for _??_1/2, 1/2. We also approximate the density for the mean corrected estmator _??_c1 c2.
