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Asymptotic expansion of the risk of maximum likelihood estimator with respect to α-divergence

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  • Yo Sheena

Abstract

For a given parametric probability model, we consider the risk of the maximum likelihood estimator with respect to α-divergence, which includes the special cases of Kullback–Leibler divergence, the Hellinger distance, and essentially χ2-divergence. The asymptotic expansion of the risk is given with respect to sample sizes up to order n− 2. Each term in the expansion is expressed with the geometrical properties of the Riemannian manifold formed by the parametric probability model.

Suggested Citation

  • Yo Sheena, 2018. "Asymptotic expansion of the risk of maximum likelihood estimator with respect to α-divergence," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(16), pages 4059-4087, August.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:16:p:4059-4087
    DOI: 10.1080/03610926.2017.1380828
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