Linear minimax regret estimation of deterministic parameters with bounded data uncertainties
Eldar, Y.C.
Ben-Tal, A.
Nemirovski, A.
Dept. of Electr. Eng., Technion - Israel Inst. of Technol., Haifa, Israel;
This paper appears in: Signal Processing, IEEE Transactions on
Publication Date: Aug. 2004
Volume: 52,
Issue: 8
On page(s): 2177- 2188
ISSN: 1053-587X
INSPEC Accession Number: 8124526
DOI: 10.1109/TSP.2004.831144
Posted online: 2004-07-19 11:11:12.0
Abstract
We develop a new linear estimator for estimating an unknown parameter vector x in a linear model in the presence of bounded data uncertainties. The estimator is designed to minimize the worst-case regret over all bounded data vectors, namely, the worst-case difference between the mean-squared error (MSE) attainable using a linear estimator that does not know the true parameters x and the optimal MSE attained using a linear estimator that knows x. We demonstrate through several examples that the minimax regret estimator can significantly increase the performance over the conventional least-squares estimator, as well as several other least-squares alternatives.
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