Efficient Estimation of a Regression Parameter for Certain Second Order Processes

Abstract

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.