A minimax Chebyshev estimator for bounded error estimation

Yonina C. Eldar*, Amir Beck, Marc Teboulle

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

48 Scopus citations

Abstract

We develop a nonlinear minimax estimator for the classical linear regression model assuming that the true parameter vector lies in an intersection of ellipsoids. We seek an estimate that minimizes the worst-case estimation error over the given parameter set. Since this problem is intractable, we approximate it using semidefinite relaxation, and refer to the resulting estimate as the relaxed Chebyshev center (RCC). We show that the RCC is unique and feasible, meaning it is consistent with the prior information. We then prove that the constrained least-squares (CLS) estimate for this problem can also be obtained as a relaxation of the Chebyshev center, that is looser than the RCC. Finally, we demonstrate through simulations that the RCC can significantly improve the estimation error over the CLS method.

Original languageEnglish
Pages (from-to)1388-1397
Number of pages10
JournalIEEE Transactions on Signal Processing
Volume56
Issue number4
DOIs
StatePublished - Apr 2008

Funding

FundersFunder number
Israel Science Foundation536-04, 489-06

    Keywords

    • Bounded error estimation
    • Chebyshev center
    • Constrained least-squares
    • Semidefinite programming
    • Semidefinite relaxation

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