Asymptotic Efficiency in Polynomial Estimation
1. Summary. Asymptotic formulas are obtained for the generalized variance of the least squares estimates in polynomial regression under the assumption that the basic random variables are those of a stationary stochastic process, or a slight generalization of such a process. These formulas are used to study the information obtained by increasing the number of observational points in an interval and by increasing the length of the interval. 2. Introduction. In an earlier paper [1], some limited -results were obtained on the increased efficiency of estimation in polynomial regression due. to increasing the number of observational points, under the assumption that the basic random variables are correlated. These results were for two special stochastic processes only. In this paper, somewh-at more general stochastic processes are studied and corresponding asymptotic formulas are obtained. The same notation will be used here as in [1]. Thus, yi , Y2, * , y. will denote random variables associated with the fixed values xl, x2, ***, x., and the regression polynomial will be denoted by