APPROXIMATION FOR DENSITY OF ESTIMATORS IN GAUSSIAN AR (1) PROCESS

抄録

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}.