Asymptotic distributions of phi-divergences of hypothetical and observed frequencies on refined partitions
dc.contributor.author | Menéndez Calleja, María Luisa | |
dc.contributor.author | Morales González, Domingo | |
dc.contributor.author | Pardo Llorente, Leandro | |
dc.contributor.author | Vadja, Igor | |
dc.date.accessioned | 2023-06-20T17:09:57Z | |
dc.date.available | 2023-06-20T17:09:57Z | |
dc.date.issued | 1988-03 | |
dc.description.abstract | For a wide class of goodness-of-fit statistics based on phi-divergences between hypothetical cell probabilities and observed relative frequencies, the asymptotic normality is established under the assumption n/m(n) --> gamma is an element of (0, infinity), where n denotes sample size and m(n) the number of cells. Related problems of asymptotic distributions of phi-divergence errors, and of phi-divergence deviations of histogram estimators from their expected values, are considered too. | |
dc.description.department | Depto. de Estadística e Investigación Operativa | |
dc.description.faculty | Fac. de Ciencias Matemáticas | |
dc.description.refereed | TRUE | |
dc.description.sponsorship | DGICYT | |
dc.description.sponsorship | Agency of Czech Republic | |
dc.description.sponsorship | COPERNICUS | |
dc.description.status | pub | |
dc.eprint.id | https://eprints.ucm.es/id/eprint/18095 | |
dc.identifier.citation | Ali,S.M. and S.D.Silvey(1966), A general class of coefficients of one distribution from another, Journal of the Royal Satatistical Society, Serie B 28, 131-142. Barron, A.R., L.Giörfy and E.C. van der Meulen(1992), Distribution estimation consistent in total variation and in two types of information divergence, Transcriptions or IEEE on Information Theory 38, 1437-1454. Beirlant, J.,L.Giörfy, Pitman efficiencies of L p-goodness-of-fit tests, Kybernetika 30, 223-232. Beirlant, J.,L.Giörfy and G.Lugosi(1994), On the asymptotic normality on the L1 and L2-errors in histogram density estimation, Canadian Journal of Statistics 22, 309-318. Beirlant, J.,and D.M.Mason(1995), On the asymptotic normality of the L p norms of empirical functions, Mathematical Methods of Statistics 4, 1-19. Berlinet, A.,L.Devroye and L.Giörfy(1995), Asymptotic normality of L1-error in density estimation, Statistics 26,319-343. Berlinet, A.,L.Giörfy and E.C. van der Meulen(1996). Asymptotic normality of relative entropy in multivariate density estimation (submitted). Bickel,P.J. and M.Rosenblatt(1973), On some global measures of the deviations of density function estimates, Annals of Statistics 1, 1071-1095. Cochran,W.G.(1952), The X-cuadrado test of goodness of fit, Annals of Mathematical Statistics 23, 315-345. Csiszár,I.(1963) Eine Informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markofoffschen Ketten, Publications of the Mathematical Institute of Hungarian academy of Sciences, Series A 8, 85-108. L.Devroye and L.Giörfy(1985), Nonparametric density estimation: the L 1-view. Wiley, New York. Giörfy,L. and E.C. van der Meulen(1991), A consitent goodness-of-fit test based on the total variation distance, in: G.Roussas(ed), Nonparametric functional estimation and related topics, Kluwer, Boston, 631-646. Giörfy,L.,F.Liese, I.Vadja and E.C. van der Meulen(1996), Distribution estimates consistent in X2-divergence (submitted). Hall,P.(1987), On Kullback-Leibler loss and density estimation, Annals of Statistics 15, 1491-1519. Hall,P.(1990),Akaike's information criterion and Kullback-Leibler loss for histogram density estimation, Probability Theory and Related Fields 85, 449-467. Holst,L.(1972), Asymptotic normality and efficiency for certain goodness-of-fit tests, Biometrika 59, 139-145. Ivchenko,G.I. and Y.I.Medvedev(1978), Separate statistics and hypothesis testing. The case of small samples, Theory of Probability and its Applications 23, 764-775. Lancaster, H.O.(1969), The chi-squared distribution, John Wiley, New York. Liese,F. and I.Vadja(1987), Convex statistical distances, Teubner Verlag, Leipzig. Morales,D.,L.Pardo and I.Vadja(1995), Asymptotic divergence of estimates of discrete distributions, Journal of Satistical Planning and Inference 48, 347-369. Morris,C.(1975), Central limit theorems for multinomial sums, Annals of Statistics 3, 165-188. Read,R.C. and N.A.C.Cressie(1988),Goodness-of-fit statistics for discrete multivariate data, Springer Verlag, New York. Rényi,A.(1961), On measures of entropy and information, Proceedings of the Fourth Berkeley Symposium on Probability Theory and Mathematical Statistics, Vol.1, 547-561. Scott,D.W.(1992), Multivariate density estimation, Wiley, New York. Silverman,B.W.(1986), Density estimation for statistics and data analisys, Chapman and Hall, London. Vadja,I.(1973),X a -divergence and generalize Fisher's information, Transcriptions of the 6th Prague Conference on Information Theory, Academia, Praha, 873-886. | |
dc.identifier.doi | 10.1111/1467-9574.00069 | |
dc.identifier.issn | 0039-0402 | |
dc.identifier.officialurl | http://onlinelibrary.wiley.com/doi/10.1111/1467-9574.00069/pdf | |
dc.identifier.relatedurl | http://onlinelibrary.wiley.com/ | |
dc.identifier.uri | https://hdl.handle.net/20.500.14352/57875 | |
dc.issue.number | 1 | |
dc.journal.title | Statistica Neerlandica | |
dc.language.iso | eng | |
dc.page.final | 89 | |
dc.page.initial | 71 | |
dc.publisher | BLACKWELL | |
dc.rights.accessRights | restricted access | |
dc.subject.cdu | 519.2 | |
dc.subject.keyword | goodness-of-fit | |
dc.subject.keyword | sparse testing schemes | |
dc.subject.keyword | histogram estimates | |
dc.subject.keyword | divergence errors | |
dc.subject.keyword | L(p)-errors | |
dc.subject.keyword | asymptotic distributions | |
dc.subject.keyword | histogram density-estimation | |
dc.subject.keyword | kullback-leibler loss | |
dc.subject.ucm | Estadística aplicada | |
dc.title | Asymptotic distributions of phi-divergences of hypothetical and observed frequencies on refined partitions | |
dc.type | journal article | |
dc.volume.number | 52 | |
dspace.entity.type | Publication | |
relation.isAuthorOfPublication | 4d5cedd9-975b-43fb-bc2e-f55dec36a2bf | |
relation.isAuthorOfPublication | a6409cba-03ce-4c3b-af08-e673b7b2bf58 | |
relation.isAuthorOfPublication.latestForDiscovery | 4d5cedd9-975b-43fb-bc2e-f55dec36a2bf |
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