Measure-Transformed Quasi-Maximum Likelihood Estimation

Koby Todros, Alfred O. Hero

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


In this paper, the Gaussian quasi-maximum likelihood estimator (GQMLE) is generalized by applying a transform to the probability distribution of the data. The proposed estimator, called measure-transformed GQMLE (MT-GQMLE), minimizes the empirical Kullback-Leibler divergence between a transformed probability distribution of the data and a hypothesized Gaussian probability measure. By judicious choice of the transform we show that, unlike the GQMLE, the proposed estimator can gain sensitivity to higher order statistical moments and resilience to outliers leading to significant mitigation of the model mismatch effect on the estimates. Under some mild regularity conditions, we show that the MT-GQMLE is consistent, asymptotically normal and unbiased. Furthermore, we derive a necessary and sufficient condition for asymptotic efficiency. A data driven procedure for optimal selection of the measure transformation parameters is developed that minimizes the trace of an empirical estimate of the asymptotic mean-squared-error matrix. The MT-GQMLE is applied to linear regression and source localization and numerical comparisons illustrate its robustness and resilience to outliers.

Original languageEnglish
Article number7707462
Pages (from-to)748-763
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number3
StatePublished - 1 Feb 2017


  • Robust estimation
  • gain estimation
  • higher-order statistics
  • probability measure transform
  • quasi maximum likelihood estimation
  • source localization

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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