Maximum likelihood estimation in linear models with a Gaussian model matrix

Author

Wiesel, Ami ; Eldar, Yonina C. ; Beck, Amir

Author_Institution

Dept. of Electr. Eng., Israel Inst. of Technol., Haifa, Israel

Volume

13

Issue

5

fYear

2006

fDate

5/1/2006 12:00:00 AM

Firstpage

292

Lastpage

295

Abstract

We consider the problem of estimating an unknown deterministic parameter vector in a linear model with a Gaussian model matrix. We derive the maximum likelihood (ML) estimator for this problem and show that it can be found using a simple line-search over a unimodal function that can be efficiently evaluated. We then discuss the similarity between the ML, the total least squares (TLS), the regularized TLS, and the expected least squares estimators.

Keywords

Gaussian processes; matrix algebra; maximum likelihood estimation; multidimensional signal processing; search problems; Gaussian model matrix; TLS; line-search; linear model; maximum likelihood estimator; total least square; unimodal function; Ambient intelligence; Array signal processing; Gaussian noise; Least squares approximation; Maximum likelihood estimation; Minimax techniques; Robustness; Statistics; Uncertainty; Vectors; Errors in variables (EIV); linear models; maximum likelihood (ML) estimation; random model matrix; total least squares (TLS);

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2006.870377

Filename

1618700