Publication:
Testing stationary distributions of Markov chains based on Rao's divergence

Loading...
Thumbnail Image
Full text at PDC
Publication Date
1999-01
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Pergamon-Elsevier Science Ltd
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
Statistical inference problems such as the estimation of parameters and testing composite hypothesis about stationary distributions in the set of states of Markov chains are solved. Both, the estimator and the statistic proposed are based on Rao's divergence. The asymptotic properties of the estimator and the critical values of asymptotically γ-level tests are obtained.
Description
This work was supported by Grants DGICYT PB96-0635 and PR156/97-7159.
Unesco subjects
Keywords
Citation
S. Tavaré, P.M.E. Altham, Serial dependence of observations leading to contingency tables, and corrections to chi-squared statistics. Biometrika, 70 (1983), pp. 139–144 M.L. Menéndez, D. Morales, L. Pardo, I. Vajda, Testing in stationary models based on f-divergences of observed and theoretical frequencies. Kybernetika, 33 (5) (1997), pp. 465–475 I. Csiszár, Eine Informationtheoretische Ungleichung und ihre Anwendung auf den Bewis der Ergodizität von Markhoffschen Ketten. Publ. Math. Inst. Hungar. Acad. Sci., 8 (1963), pp. 85–108 Ser. A M. C. Pardo, Goodness- of- fit tests for stationary distributions of Markov chains based on Rao's divergence. Information Sciences (1998) J. Burbea, C.R. Rao, On the convexity of some divergence measures based on entropy functions. IEEE Transactions on Information Theory, 28 (1982), pp. 489–495 M.C. Pardo, On Burbea-Rao divergences based goodness-of-fit tests for multinomial models (to appear). M.C. Pardo, Goodness-of-fit tests based on Rao's divergence under sparseness assumptions (to appear). M.C. Pardo, I. Vajda, About distances of discrete distributions satisfying the data proccesing theorem of information theory. Trans. IEEE on Inform. Theory, 43 (4) (1997), pp. 1288–1293 M.L. Menéndez, D. Morales, L. Pardo and I. Vajda, Inference about stationary distributions of Markov chains based on divergences with observed frequencies, Probability and Mathematical Statistics (to appear). P. Billingsley, Statistical methods in Markov chains. Ann. Math. Statist., 32 (1961), pp. 12–40 M.W.Birch,A new proof of the Pearson-Fisher theorem. Annals of Mathematical Statistics, 35 (1964), pp. 817–824 Y.M.M. Bishop, S.E. Fienberg, P.W. Holland, Discrete Multivariate Analysis Theory and Practice. The MIT Press, Cambridge, MA (1975) T.R.C. Read, N. Cressie, Goodness of Fit Statistics for Discrete Multivariate Data. Springer, New York (1988) D. Morales, L. Pardo, I. Vajda, Asymptotic divergence of estimates of discrete distributions. Journal of Statistical Planning and Inference, 48 (1995), pp. 347–369 M.C. Pardo, Asymptotic behaviour of an estimator based on Rao's divergence. Kybernetika, 33 (5) (1997), pp. 489–504 S. Kotz, N.M. Johnson, D.W. Boid, Series representation of quadratic forms in normal variables,I.Central case AMS(1967), pp. 823–837 J.N.K. Rao, A.J. Scott, The analysis of categorical data from complex sample surveys: Chi-squared tests for goodness of fit and independence in two-way tables. J. Amer. Stat. Assoc., 76 (1981), pp. 221–230 F.E. Satterthwaite, An aproximate distribution of estimates of variance components. Biometrics, 2 (1946), pp. 110–114 H. Scheffé, The Analysis of Variance. Wiley (1959)
Collections