Open Access
December, 1961 Efficient Estimation of a Regression Parameter for Certain Second Order Processes
Charlotte T. Striebel
Ann. Math. Statist. 32(4): 1299-1313 (December, 1961). DOI: 10.1214/aoms/1177704868


The problem of estimation of a single regression parameter for a process with fixed known regression function and unknown covariance is attacked using a Hilbert space representation of the process. Some general results are obtained which characterize efficiency classes of covariances--that is, classes for each of which there exists a single estimate that is efficient for all members. These results are applied to both the discrete parameter and the continuous parameter stationary process with rational spectral density. Some special results are also obtained concerning the efficiency of the least square estimate.


Download Citation

Charlotte T. Striebel. "Efficient Estimation of a Regression Parameter for Certain Second Order Processes." Ann. Math. Statist. 32 (4) 1299 - 1313, December, 1961.


Published: December, 1961
First available in Project Euclid: 27 April 2007

zbMATH: 0109.12901
MathSciNet: MR143297
Digital Object Identifier: 10.1214/aoms/1177704868

Rights: Copyright © 1961 Institute of Mathematical Statistics

Vol.32 • No. 4 • December, 1961
Back to Top