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Some information inequalities for statistical inference

Author

Listed:
  • K. V. Harsha

    (Indian Institute of Technology Bombay)

  • Alladi Subramanyam

    (Indian Institute of Technology Bombay)

Abstract

In this paper, we first describe the generalized notion of Cramer–Rao lower bound obtained by Naudts (J Inequal Pure Appl Math 5(4), Article 102, 2004) using two families of probability density functions: the original model and an escort model. We reinterpret the results in Naudts (2004) from a statistical point of view and obtain some interesting examples in which this bound is attained. Further, we obtain information inequalities which generalize the classical Bhattacharyya bounds in both regular and non-regular cases.

Suggested Citation

  • K. V. Harsha & Alladi Subramanyam, 2020. "Some information inequalities for statistical inference," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1237-1256, October.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:5:d:10.1007_s10463-019-00725-3
    DOI: 10.1007/s10463-019-00725-3
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    References listed on IDEAS

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    1. Amari, Shun-ichi & Ohara, Atsumi & Matsuzoe, Hiroshi, 2012. "Geometry of deformed exponential families: Invariant, dually-flat and conformal geometries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4308-4319.
    2. K.V., Harsha & K.S., Subrahamanian Moosath, 2015. "Dually flat geometries of the deformed exponential family," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 136-147.
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