1988 Volume 18 Issue 2 Pages 107-121
In time series inference for a spectral parameter, asymptotic ancillary statistic is constructed in terms of the maximum likelihood estimator and the observed Fisher information. It is shown that this ancillary statistic is second-order locally ancillary. Then we give a sufficient condition that the modified ancillary statistic is second-order asymptotically ancillary. Also the second-order Edgeworth expansion of the conditional distribution of the maximum likelihood estimator given the ancillary statistic is evaluated. Using this Edgeworth expansion we can calculate confidence intervals with probability levels to O(1/n), where n is the sample size. Then we investigate how the ancillary statistic gives suggestions. Some numerical studies are made and they show that our second-order approximation for the distribution of the ancillary statistic is good.
