References: |
Amari S. (1982a) Differential geometry of curved exponential families – curvatures and information loss, Ann. Statist., 10:357-387. Amari S. (1982b) Geometrical theory of asymptotic ancillarity and conditional inference, Biometrika, 69: 1-17. Amari S. (1990) Differential-Geometric Methods in Statistics, Lecture Notes in Statistics 28, (first edition 1985), Springer-Verlag: Berlin. Amari S., Barndorff-Nielsen O. E., Kass R. E., Lauritzen S. L. and Rao C. R. (1987) Differential Geometry in Statistical Inference, Institute of Mathematical Statistics, Hayward: California. Amari S. and Kumon M. (1983) Differential geometry of Edgeworth expansions in curved exponential families, Ann. Inst. Statist. Math., 35A:1-24. Amari S. and Kumon M. (1988) Estimation in the presence of infinitely many nuisance parameters – geometry of estimating functions, Ann. Statist., 16:1044-1068. Amari S., Kurata K. and Nagaoka H. (1990) Differential geometry of Boltzmann machines, Technical Report METR 90-19, Dept. Mathematical Engineering, University of Tokyo. Atkinson C. and Mitchell A. F. S. (1981) Rao’s distance measure, Sankhya, A, 43:345-365. Barndorff-Nielsen O. E. (1983) On a formula for the distribution of the maximum likelihood estimator, Biometrika, 70:343-365. Barndorff-Nielsen O. E. (1986) Likelihood and observed geometries, Ann. Statist., 14:856-873. Barndorff-Nielsen O. E. (1987a) Differential and integral geometry in statistical inference, In: Differential Geometry in Statistical Inference, (Amari S., Barndorff-Nielsen O. E., Kass R. E., Lauritzen S. L. and Rao C. R.), Institute of Mathematical Statistics, Hayward: California, 95-161. Barndorff-Nielsen O. E. (1987b) Differential geometry and statistics: some mathematical aspects, Indian J. Math., 29:335-350. Barndorff-Nielsen O. E. (1988) Parametric Statistical Models and Likelihood, Lecture Notes in Statistics 50, Springer-Verlag: Berlin. Barndorff-Nielsen O. E. and Blaesild P. (1987a) Strings: mathematical theory and statistical aspects, Proc. Roy. Soc. London, A, 411:155-176. Barndorff-Nielsen O. E. and Blaesild P. (1987b) Derivative strings: contravariant aspects, Proc. Roy. Soc. London, A, 411:421-444. Barndorff-Nielsen O. E. and Blaesild P. (1988) Coordinate-free definition of structurally symmetric derivative strings, Adv. Appl. Math., 9:1-6. Barndorff-Nielsen O. E. and Cox D. R. (1989) Asymptotic Techniques for Use in Statistics, Chapman and Hall: London. Barndorff-Nielsen O. E. and Cox D. R. (1994) Inference and Asymptotics, Chapman and Hall: London. Barndorff-Nielsen O. E., Cox D. R. and Reid N. (1986) The rôle of differential geometry in statistical theory, Int. Statist. Rev., 54:83-96. Bates D. M. and Watts D. G. (1980) Relative curvature measures of nonlinearity, J. Roy. Statist. Soc., B, 42:1-25. Bates D. M. and Watts D. G. (1981) Parameter transformations for improved approximate confidence intervals in nonlinear least squares, Ann. Statist., 9:1152-1167. Bhattacharrya A. (1943) On discrimination and divergence, In: Proc. 29th Indian Sci. Cong., 13, Part III. Bhattacharrya A. (1946) On a measure of divergence between two multinomial populations, Sankhya, 7:401-406. Burbea J. and Rao C. R. (1982a) Entropy differential metrics, distance and divergence measures in probability spaces: a unified approach, J. Multivariate Analysis, 12:575-596. Burbea J. and Rao C. R. (1982b) On the convexity of some divergence measures based on entropy functions, IEEE Trans. on Inf. Theory, 28:489-495. Chentsov N. N. (1972) Statistical Decision Rules and Optimal Inference, Nuaka:Moscow; translated from Russian into English (1982), AMS, Rhode Island. Cook R. D. (1986) Assessment of local influence (with Discussion), J. Roy. Statist. Soc., B, 48:133-169. Critchley F. (1998) Discussion of Some algebra and geometry for hierarchical models, applied to diagnostics by J. S. Hodges, J. Roy. Statist. Soc., B, 60:528-529. Critchley F., Marriott P. K. and Salmon M. H. (1992) Distances in statistics, Proc. 36th Meeting Italian Statist. Soc., CISU: Rome, 36-60. Critchley F., Marriott P. K. and Salmon M. H. (1993) Preferred point geometry and statistical manifolds, Ann. Statist., 21:1197-1224. Critchley F., Marriott P. K. and Salmon M. H. (1994) Preferred point geometry and the local differential geometry of the Kullback-Leibler divergence, Ann. Statist., 22:1587-1602. Critchley F., Marriott P. K. and Salmon M. H. (1999) An elementary treatment of Amari’s expected geometry, In: Applications of Differential Geometry to Econometrics, Marriott P. K. and Salmon M. H. (Eds.), Cambridge University Press, (to appear). Dawid A. P. (1975) Discussion of Efron’s paper, Ann. Statist., 3:1231-1234. Dawid A. P. (1977) Further comments on a paper by Bradley Efron, Ann. Statist., 5:1249. Efron B. (1975) Defining the curvature of a statistical problem (with Discussion), Ann. Statist., 3:1189-1217. Efron B. (1978) The geometry of exponential families, Ann. Statist., 6:362-376. Eguchi S. (1983) Second order efficiency of minimum contrast estimators in a curved exponential family, Ann. Statist., 11:793-803. Eguchi S. (1984) A characterisation of second order efficiency in a curved exponential family, Ann. Inst. Statist. Math., 36A:199-206. Eguchi S. (1991) A geometric look at nuisance parameter effect of local powers in testing hypotheses, Ann. Inst. Statist. Math., 43A:245-260. Jeffreys H. (1948) Theory of Probability, (second edition), Clarendon Press: Oxford. Kass R. E. (1984) Canonical parameterizations and zero parameter effects curvature, J. Roy. Statist. Soc., B, 46:86-92. Kass R. E. (1989) The geometry of asymptotic inference (with Discussion), Statistical Science, 4:188-234. Kass R. E. (1990) Data-translated likelihoods and Jeffrey’s rules, Biometrika, 77:107-114. Kass R. E. and Vos P. W. (1997) Geometrical Foundations of Asymptotic Inference, John Wiley: New York. Kullback S. L. and Leibler R. A. (1951) On information and sufficiency, Ann. Math. Statist., 22:79-86. Lauritzen S. L. (1987) Statistical manifolds, In: Differential Geometry in Statistical Inference, (Amari S., Barndorff-Nielsen O. E., Kass R. E., Lauritzen S. L. and Rao C. R.), Institute of Mathematical Statistics, Hayward: California, 163-216. Loynes R. L. (1986) Discussion of Assessment of local influence by R. D. Cook, J. Roy. Statist. Soc., B, 48:156-157. Marriott P. K. (1989) Applications of Differential Geometry to Statistics, PhD thesis, University of Warwick. Murray M. K. and Rice J. W. (1993) Differential Geometry and Statistics, Chapman and Hall: London. Oller J. M. and Corcuera J. M. (1995) Intrinsic analysis of statistical estimation, Ann. Statist., 23:1562-1581. Oller J. M. and Cuadras C. M. (1985) Rao’s distance for negative multinomial distributions, Sankhya, A, 47:75-83. Pistone G. and Sempi C. (1995) An infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one, Ann. Statist., 23:1543-1561. Rao C. R. (1945) Information and accuracy attainable in the estimation of statistical parameters, Bull. Calcutta Math. Soc., 37:81-89. Rao C. R. (1961) Asymptotic information and limiting information, In: Proc. Fourth Berkeley Symp. Math. Statist. Probab., 1:531-545. Rao C. R. (1962) Efficient estimates and optimum inference procedures in large samples (with Discussion), J. Roy. Statist. Soc., B, 24:46-72. Rao C. R. (1963) Criteria of estimation in large samples, Sankhya, A, 25:189-206. Rao C. R. (1987) Differential metrics in probability spaces, In: Differential Geometry in Statistical Inference, (Amari S., Barndorff-Nielsen O. E., Kass R. E., Lauritzen S. L. and Rao C. R.), Institute of Mathematical Statistics, Hayward: California, 217-240. Rao C. R., Sinha B. K. and Subramanyam K. (1982) Third order efficiency of the maximum likelihood estimator in the multinomial distribution, Statistics and Decisions, 1:1-16. Vos P. W. (1989) Fundamental equations for statistical submanifolds with applications to the Bartlett correction, Ann. Inst. Statist. Math., 41:429-450. Vos P. W. (1991a) Geometry of f-divergence, Ann. Inst. Statist. Math., 43:515-537. Vos P. W. (1991b) A geometrical approach to identifying influential cases, Ann. Statist., 19:1570-1581. Vos P. W. (1992) Minimum f-divergence estimators and quasi-likelihood functions, Ann. Inst. Statist. Math., 44:261-279. Vos P. W. (1994) Likelihood-based measures of influence for generalized linear models, Communications in Statistics, A, 23:3477-3490. Zhu H. T. and Wei B. C. (1997a) Some notes on preferred point alpha-geometry and alpha-divergence function, Statistics and Probability Letters, 33:427-437. Zhu H. T. and Wei B. C. (1997b) Preferred point alpha-manifold and Amari’s alpha-connections, Statistics and Probability Letters, 36:219-229. |