Open Access
December, 1958 Efficiency Problems in Polynomial Estimation
Paul G. Hoel
Ann. Math. Statist. 29(4): 1134-1145 (December, 1958). DOI: 10.1214/aoms/1177706446


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.


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Paul G. Hoel. "Efficiency Problems in Polynomial Estimation." Ann. Math. Statist. 29 (4) 1134 - 1145, December, 1958.


Published: December, 1958
First available in Project Euclid: 27 April 2007

zbMATH: 0094.14501
MathSciNet: MR100934
Digital Object Identifier: 10.1214/aoms/1177706446

Rights: Copyright © 1958 Institute of Mathematical Statistics

Vol.29 • No. 4 • December, 1958
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