Parameter bounds on estimation accuracy under model misspecification

Christ D. Richmond, Larry L. Horowitz

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


When the assumed data distribution differs from the true distribution, the model is said to be misspecified or mismatched. Model misspecification at some level is an inevitability of engineering practice. While Huber's celebrated work assesses maximum-likelihood (ML) performance under misspecification, no simple theory for bounding parameter estimation exists. The class of parameter bounds emerging from the covariance inequality, or equivalently the minimum norm theorem is revisited. The expectation operator is well-known to form an inner product space. Flexibility in the choice of expectation integrand and measure for integration exists, however, to establish a class of parameter bounds under a general form of model misspecification, i.e., distribution mismatch. The Cramér-Rao bound (CRB) primarily, and secondarily the Barankin/Hammersley-Chapman-Robbins, Bhattacharyya, and Bobrovsky-Mayer-Wolf-Zakai bounds under misspecification are considered. Huber's sandwich covariance is readily established as a special case of the misspecified CRB subject to ML constraints, and generalizations of the Slepian and Bangs formulae under misspecification are obtained.

Original languageEnglish (US)
Article number7055906
Pages (from-to)2263-2278
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number9
StatePublished - May 1 2015
Externally publishedYes


  • Covariance inequality
  • Cramér-Rao
  • Slepian-Bangs
  • mismatch
  • misspecification
  • misspecified model
  • parameter bound
  • sandwich covariance

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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