Differential Geometry in Statistical Inference

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Page 238 - Entropy differential metric, distance and divergence measures in probability spaces: A unified approach, J.
Page 93 - Second order efficiency of minimum contrast estimators in a curved exponential family.
Page 240 - Convexity properties of entropy functions and analysis of diversity. In Inequalities in Statistics and Probability, IMS Lecture Notes, 5, 68-77.
Page 90 - Acknowledgements The author would like to express his sincere gratitude to Dr.
Page 161 - A note on the inverse Gaussian distribution function. J. Amer. Statist. Assoc. 63, 1514-1516.
Page 91 - Estimation of a structural parameter in the presence of a large number of nuisance parameters, Biometnka 71.
Page 21 - Wiener processes, and so on, have so far been studied in detail, it seems rather strange that only a few theories have been proposed concerning properties of a family itself of distributions. Here, by the properties of a family we mean such geometric relations as mutual distances, flatness or curvature of the family, etc.
Page 94 - Nagaoka, H. and Amari, S. (1982). Differential geometry of smooth families of probability distributions, METR 82-7, Univ. Tokyo.
Page 14 - This paper was prepared with support from the National Science Foundation under Grant No.
Page 240 - Radhakrishna and Nayak, TK (1985). Cross entropy, dissimilarity measures and characterizations of quadratic entropy.