Least Squares and Linear Unbiased Minimum Variance Estimation in Euclidean Space and Hilbert Space.

摘要

The estimation of an unknown vector-valued parameter in a linear model with additive noise is treated. The least-squares theory is given for the case both parameter and observation are elements of Hilbert space,and the solution is put in recursive form. A Gauss-Markov type theorem for linear unbiased minimum variance estimation is proved,again for the case both parameter and observation are elements of Hilbert space,and the solution is put in recursive form for the finite-dimensional case only. A modification of the linear unbiased minimum variance estimate which accounts for some prior information is given. (Author)