APPROXIMATIONS FOR THE BIAS AND THE VARIANCE OF A CLASS OF NONRECURSIVE AUTOREGRESSIVE ESTIMATORS

Abstract

The quality of autoregressive estimators can be judged by statistical criteria like the bias and the variance of the estimated parameters. But generally, analytical expressions for these criteria exist only in the asymptotic case of great samples. - This paper presents a class of nonrecursive autoregressive estimators which contains most of the usually used autoregressive estimators, especially the Orthogonal Regression. A statistical linearization of this class leads to approximations for the quality criteria. They are valid for every sample size, but only for small disturbances. Further, there are hints about a good estimation depending on the effective sampling time in the autoregressive equation.