Abstract
Maximum quasi-likelihood estimators have several nice asymptotic properties. We show that, in many situations, a family of estimators, called the minimum f-divergence estimators, can be defined such that each estimator has the same asymptotic properties as the maximum quasi-likelihood estimator. The family of minimum f-divergence estimators include the maximum quasi-likelihood estimators as a special case. When a quasi-likelihood is the log likelihood from some exponential family, Amari's dual geometries can be used to study the maximum likelihood estimator. A dual geometric structure can also be defined for more general quasi-likelihood functions as well as for the larger family of minimum f-divergence estimators. The relationship between the f-divergence and the quasi-likelihood function and the relationship between the f-divergence and the power divergence is discussed.
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This work was supported by National Science Foundation grant DMS 88-03584.
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Vos, P.W. Minimum f-divergence estimators and quasi-likelihood functions. Ann Inst Stat Math 44, 261–279 (1992). https://doi.org/10.1007/BF00058640
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DOI: https://doi.org/10.1007/BF00058640