Publication: Renyi statistics in directed families of exponential experiments
No Thumbnail Available
Full text at PDC
Advisors (or tutors)
Taylor & Francis
Renyi statistics are considered in a directed family of general exponential models. These statistics are defined as Renyi distances between estimated and hypothetical model. An asymptotically quadratic approximation to the Renyi Statistics is established, leading to similar asymptotic distribution results as established in the literature For the likelihood ratio statistics. Some arguments in favour of the Renyi statistics are discussed, and a numerical comparison of the Renyi goodness-of-fit tests with the Likelihood ratio test is presented.
Barndorff-Nielsen, O. E. (1978) Information and Exponential Families. J. Wiley, Gluchester. Barndorff-Nielsen, O. E. and Sørensen, M. (1991) Information quantities in non classical settings. Computational Statistics and Data Analysis, 12, 143–158. Barndorff-Nielsen, O. E. and Sørensen, M. (1994) A review of some aspects of asymptotic likelihood theory for stochastic processes. International Statistical Review, 62, 133–165. Bhattacharyya, A. (1946) On some analogues to the amount of information and their uses in statistical estimation. Sankhya, 8, 1–14. Bertrand, P. and Kutoyants, Yu. A. (1996) A minimum distance estimator for partially observed linear stochastic systems. Statistics and Decisions, 14, 323–342. Brown, L. D. (1986) Fundamentals of Statistical Exponential Families. Lecture Notes Vol. 9. Institute of Mathematical Statistics, Hayward, California. Falk, M., Hüsler, J. and Reiss, R. D. (1994) Laws of Small Numbers: Extremes and Rare Events. Birkhäuser, Berlin. Gidas, B. (1991) Parametric estimation for gibbs distributions I: Fully observed data. Markov Random Fields: Theory and Applications (Eds. Jain and Chellapa). Academic Press, New York. Guyon, X. (1995) Random Fields on a Network. Springer, Berlin. Janzura, M. (1988) Statistical Analysis of Gibbs Random Fields. Trans. 10-th Prague Conf. in Inform. Th. Statist. Dec. Funct., Random Proc., pp. 429–438. Reidel, Amsterdam. Küchler, U. and Sørensen, M. (1994) Exponential families of stochastic processes and Lévy processes. Journal of Statistical Planning and Inference, 39, 211–237. Küchler, U. and Sørensen, M. (1997) Exponential Families of Stochastic Processes. Springer, Berlin. Kutoyants, Yu. A. (1984) Parameter Estimation for Stochastic Processes. Hel-derman, Berlin. Kutoyants, Yu. A. (1994) Identification and Dynamical Systems with Small Noise. Kluwer, Dordrecht. Liese, F. and Vajda, I. (1987) Convex Statistical Distances. Teubner, Leipzig. Menéndez, M. L., Morales, D., Pardo, L. and Vajda, I. (1995) Divergence based estimation and testing of statistical models of classification. Journal of Multivariate Analysis, 54, 329–354. Morales, D., Pardo, L. and Vajda, I. (1997) Some new statistics for testing hypotheses in parametric models. Journal of Multivariate Analysis, 62, 137–168. Read, T. R. C. and Cressie, N. A. C. (1988) Goodness of Fit Statistics for Discrete Multivariate Data. Springer-Verlag. Rényi, A. (1961) On measures of entropy and information. Fourth Berkeley Symposium on Mathematics, Statistics and Probability, 1, 547–561 University of California Press, Berkeley. Vajda, I. and Jauzura, M. (1997) On asymptotically optimal estimates for general observations. Stochastic Processes and Applications, 72, 27–45.