Statistical inference for finite Markov chains based on divergences
| dc.contributor.author | Menéndez Calleja, María Luisa | |
| dc.contributor.author | Morales González, Domingo | |
| dc.contributor.author | Pardo Llorente, Leandro | |
| dc.contributor.author | Zografos, Konstantinos | |
| dc.date.accessioned | 2023-06-20T17:09:48Z | |
| dc.date.available | 2023-06-20T17:09:48Z | |
| dc.date.issued | 1999-06-01 | |
| dc.description.abstract | We consider statistical data forming sequences of states of stationary finite irreducible Markov chains, and draw statistical inference about the transition matrix. The inference consists in estimation of parameters of transition probabilities and testing simple and composite hypotheses about them. The inference is based on statistics which are suitable weighted sums of normed phi-divergences of theoretical row distributions, evaluated at suitable points, and observed empirical row distributions. The asymptotic distribution of minimum phi-divergence estimators is obtained, as well as critical values of asymptotically alpha-level tests. | |
| dc.description.department | Depto. de Estadística e Investigación Operativa | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGCYT | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/18089 | |
| dc.identifier.doi | 10.1016/S0167-7152(98)00106-0 | |
| dc.identifier.issn | 0167-7152 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0167715298001060 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57871 | |
| dc.issue.number | 1 | |
| dc.journal.title | Statistics and probability letters | |
| dc.language.iso | eng | |
| dc.page.final | 17 | |
| dc.page.initial | 9 | |
| dc.publisher | Elsevier Science Bv. | |
| dc.relation.projectID | PB93-0022 | |
| dc.relation.projectID | PB96-0635 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 519.217 | |
| dc.subject.keyword | Markov chains | |
| dc.subject.keyword | minimum distance estimates | |
| dc.subject.keyword | goodness-of-fit tests | |
| dc.subject.keyword | divergence statistics | |
| dc.subject.keyword | multinomial goodness | |
| dc.subject.keyword | distributions | |
| dc.subject.keyword | tests | |
| dc.subject.keyword | fit | |
| dc.subject.ucm | Estadística matemática (Matemáticas) | |
| dc.subject.unesco | 1209 Estadística | |
| dc.title | Statistical inference for finite Markov chains based on divergences | |
| dc.type | journal article | |
| dc.volume.number | 41 | |
| dcterms.references | Ali, S.M., Silvey, S.D., 1966. A general class of coefficient of divergence of one distribution from another. J. Roy. Statist. Soc. Ser. B 286, 131-142. Azlarov, T.A., Narkhuzhaev, A.A., 1987. Asymptotic analysis of some chi-square type tests for Markov chains. Dokl. Akad. Navk. UzSSR 7, 3-5. Azlarov, T.A., Narkhuzhaev, A.A., 1992. On asymptotic behavior of distributions of some statistics for Markov chains. Theory Probab. Appl. 37, 117-119. Basawa, I.V., Prakasa Rao, B.L.S., 1980. Statistical Inference for Stochastic Processes. Academic Press, London. Billingsley, P., 1961a. Statistical methods in Markov chains. Ann. Math. Statist. 32, 13-39. Billingsley, P., 1961b. Statistical Inference for Markov Processes. Chicago Univ. Press, Chicago Press. Birch, M.W., 1964. A new proof of the Pearson-Fisher theorem. Ann. Math. Statist. 35, 817-824. Bishop, Y.M.M., Fienberg, S.E., Holland, P.W., 1975. Discrete Multivariate Analysis. Theory and Practice. The MIT Press, Cambridge, MA. Csiszár, I., 1963. Eine informationstheoretische ungleichung und ihere anwendung auf den beweis der ergodizität von Markoffschen ketten. Pub. Math. Inst. Hungarian Acad. Sci. Ser. A 8, 85-108. Cressie, N., Read, T.R.C., 1984. Multinomial goodness of fit tests. J. Roy. Statist. Soc. Ser. B 46, 440-464. Ferguson, T., 1996. A Course in Large Sample Theory. Chapman & Hall, London. Hfijek, J., Sid/tk, Z., 1967. Theory of Rank Tests. Academic Press, New York. Ivchenko, G., Medvedev, Y., 1990. Mathematical Statistics. Mir, Moscow. LeCam, L., 1960. Locally Asymptotic normal families of distribution. Univ. California Publications in Statistics. Univ. California Press, Berkeley. Liese, F., Vajda, I., 1987. Convex Statistical Distances. Teubner, Leipzig. Lifshits, B.A., 1978. On the central limit theorem for Markov chains. Theory Probab. Appl. 23, 279-296. Mirvaliev, M., Narkhuzhaer, A.A., 1990. On a chi-square test for homogeneous Markov chains. Izv. Akad. Navk. UzSSR, Ser. Fiz.-Mat. 1, 28 32. Morales, D., Pardo, L., Vajda, I., 1995. Asymptotic divergence of estimates of discrete distributions. J. Statist. Plann. Inference 48, 347-369. Parr, W.C., 1981. Minimum distance estimation: a bibliography. Comm. Statist. (Theory and Meth.) 12, 1205-1224. Read, T.R.C., Cressie, N.A.C., 1988. Goodness-of-Fit Statistics for Discrete Multi-variate Data. Springer, Berlin. Roussas, G.G., 1979. Asymptotic distribution of the log-likelihood function for stochastic processes. Z. Wahrshein. Verw. Gebiete. 47, 31-46. Salicrt, M., Morales, D., Mentndez, M.L., Pardo, L., 1994. On the applications of divergence type measures in testing statistical hypotheses. J. Multivariate Anal. 51, 372-391. Sirazhdinov, S.Kh., Formaun, Sh.K., 1983. On estimates of the rate of convergence in the central limit theorem for homogeneous Markov chains. Theory Probab. Appl. 28, 229-239. Vajda, I., 1989. Theory of Statistical Inference and Information. Kluwer, Dordrecht. Wolfowitz, J., 1953. Estimation by the minimum distance method. Ann. Inst. Statist. Math. 5, 9-23. Zografos, K., Ferentinos, K., Papaionnou, T., 1990. ~o-divergence statistics: sampling properties and multinomial goodness of fit and divergence tests. Comm. Statist. (Theory and Meth.) 19(5), 1785-1802. | |
| dspace.entity.type | Publication | |
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| relation.isAuthorOfPublication | a6409cba-03ce-4c3b-af08-e673b7b2bf58 | |
| relation.isAuthorOfPublication.latestForDiscovery | 4d5cedd9-975b-43fb-bc2e-f55dec36a2bf |
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