Reduced rank linear regression and weighted low rank approximations

This paper addresses parameter estimation in reduced rank linear regressions. This estimation problem has applications in several subject areas including system identification, sensor array processing, econometrics and statistics. A new estimation procedure, based on instrumental variable principles...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 54; no. 6; pp. 2063 - 2075
Main Authors: Werner, K., Jansson, M.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.06.2006
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
Approximation
Array signal processing
Asymptotic properties
Cramer-Rao lower bound (CRB)
CramÉr-Rao lower bound (CRB)
Design methodology
Detection, estimation, filtering, equalization, prediction
Econometrics
Exact sciences and technology
Exact solutions
factor analysis
Information, signal and communications theory
Instruments
Linear regression
Mathematical analysis
Mathematical models
matrices
Miscellaneous
Noise
parameter
Parameter estimation
rank detection
reduced rank linear regression
Regression
Sensor arrays
Sensor systems and applications
Signal and communications theory
Signal processing
Signal, noise
signals
space
Statistics
Studies
System identification
Telecommunications and information theory
weighted low rank approximation (WLRA)
Performance evaluation
Parameter estimation
Array signal processing
Linear regression
Correlated noise
Time correlation
Regression analysis
Algorithm
Statistical test
factor analysis
Unbiased estimation
Cramér-Rao lower bound (CRB)
reduced rank linear regression
weighted low rank approximation (WLRA)
Covariance
System identification
rank detection
Sensor array
Approximate solution
Rank test
Cramer Rao inequality
ISSN:1053-587X, 1941-0476, 1941-0476
Online Access:Get full text
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Description
Summary:This paper addresses parameter estimation in reduced rank linear regressions. This estimation problem has applications in several subject areas including system identification, sensor array processing, econometrics and statistics. A new estimation procedure, based on instrumental variable principles, is derived and analyzed. The proposed method is designed to handle noise that is both spatially and temporally autocorrelated. An asymptotical analysis shows that the proposed method outperforms previous methods when the noise is temporally correlated and that it is asymptotically efficient otherwise. A numerical study indicates that the performance is significantly improved also for finite sample set sizes. In addition, the Cramer-Rao lower bound (CRB) on unbiased estimator covariance for the data model is derived. A statistical test for rank determination is also developed. An important step in the new algorithm is the weighted low rank approximation (WLRA). As the WLRA lacks a closed form solution in its general form, two new, noniterative and approximate solutions are derived, both of them asymptotically optimal when part of the estimation procedure proposed here. These methods are also interesting in their own right since the WLRA has several applications.
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ISSN:1053-587X
1941-0476
1941-0476
DOI:10.1109/TSP.2006.873502