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Asymptotic cumulants of the minimum phi-divergence estimator for categorical data under possible model misspecification

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  • Haruhiko Ogasawara

Abstract

The asymptotic cumulants of the minimum phi-divergence estimators of the parameters in a model for categorical data are obtained up to the fourth order with the higher-order asymptotic variance under possible model misspecification. The corresponding asymptotic cumulants up to the third order for the studentized minimum phi-divergence estimator are also derived. These asymptotic cumulants, when a model is misspecified, depend on the form of the phi-divergence. Numerical illustrations with simulations are given for typical cases of the phi-divergence, where the maximum likelihood estimator does not necessarily give best results. Real data examples are shown using log-linear models for contingency tables.

Suggested Citation

  • Haruhiko Ogasawara, 2020. "Asymptotic cumulants of the minimum phi-divergence estimator for categorical data under possible model misspecification," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(10), pages 2448-2465, May.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:10:p:2448-2465
    DOI: 10.1080/03610926.2019.1576888
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    Cited by:

    1. Haruhiko Ogasawara, 2021. "A Unified Treatment of Agreement Coefficients and their Asymptotic Results: the Formula of the Weighted Mean of Weighted Ratios," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 390-422, July.

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