Efficiency Problems in Polynomial Estimation

Abstract

Using the generalized variance as a criterion for the efficiency of estimation, the best choice of fixed variable values within an interval for estimating the coefficients of a polynomial regression curve of given degree is determined for the classical regression model. Using this same criterion, some results are obtained on the increased efficiency arising from doubling the number of equally spaced observation points (i) when the total interval is fixed and (ii) when the total interval is doubled. Measures of the increased efficiency are found for the classical regression model and for models based on a particular stationary stochastic process and a pure birth stochastic process.