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Mean Square Error bounds for parameter estimation under model misspecification

Adria Gusi-Amig'o,P. Closas,L. Vandendorpe

Published 2015 in arXiv: Statistics Theory

ABSTRACT

In parameter estimation, assumptions about the model are typically considered which allow us to build optimal estimation methods under many statistical senses. However, it is usually the case where such models are inaccurately known or not capturing the complexity of the observed phenomenon. A natural question arises to whether we can find fundamental estimation bounds under model mismatches. This paper derives a general bound on the mean square error (MSE) following the Ziv-Zakai methodology for the widely used additive Gaussian model. The general result accounts for erroneous functionals, hyperparameters, and distributions differing from the Gaussian. The result is then particularized to gain some insight into specific problems and some illustrative examples demonstrate the predictive capabilities of the bound.

PUBLICATION RECORD

  • Publication year

    2015

  • Venue

    arXiv: Statistics Theory

  • Publication date

    2015-11-12

  • Fields of study

    Mathematics

  • Identifiers
    arXiv 1511.03982
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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