NDLI: Blind Minimax Estimation

Content Provider	IEEE Xplore Digital Library
Author	Ben-Haim, Z. Eldar, Y.C.
Copyright Year	1963
Abstract	We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded parameter set minimax estimator, whose parameter set is itself estimated from measurements. Thus, our approach does not require any prior assumption or knowledge, and the proposed estimator can be applied to any linear regression problem. We demonstrate analytically that the BMEs strictly dominate the least-squares (LS) estimator, i.e., they achieve lower mean-squared error (MSE) for any value of the parameter vector. Both Stein's estimator and its positive-part correction can be derived within the blind minimax framework. Furthermore, our approach can be readily extended to a wider class of estimation problems than Stein's estimator, which is defined only for white noise and nontransformed measurements. We show through simulations that the BMEs generally outperform previous extensions of Stein's technique.
Sponsorship	IEEE Information Theory Society
Starting Page	3145
Ending Page	3157
Page Count	13
File Size	460397
File Format	PDF
ISSN	00189448
Volume Number	53
Issue Number	9
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-09-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Minimax techniques Vectors Linear regression Noise measurement Gaussian noise Parameter estimation White noise Bayesian methods Covariance matrix linear regression model Biased estimation James–Stein estimation minimax estimation
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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