Asymptotic approximations for the distributions of the K phi-divergence goodness-of-fit statistics
| dc.contributor.author | Pérez, T. | |
| dc.contributor.author | Pardo Llorente, Julio Ángel | |
| dc.date.accessioned | 2023-06-20T09:44:50Z | |
| dc.date.available | 2023-06-20T09:44:50Z | |
| dc.date.issued | 2003-07 | |
| dc.description.abstract | K-phi-divergence's, statistic family for goodness-of-fit, under the null hypothesis, has an asymptotic chi-squared distribution; however, for small samples, the chi-squared approximation in some cases does not well agree with the exact distribution. In this paper, a closer approximation to the exact distribution is obtained by extracting the phi-dependent second order component from the distribution. Moreover, numerical results are presented for moderate sample sizes with moderate number of cells. | |
| dc.description.department | Depto. de Estadística e Investigación Operativa | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17717 | |
| dc.identifier.doi | 10.1007/s00362-003-0160-0 | |
| dc.identifier.issn | 0932-5026 | |
| dc.identifier.officialurl | http://link.springer.com/content/pdf/10.1007%2Fs00362-003-0160-0content/pdf/10.1007%2Fs00362-003-0160-0 | |
| dc.identifier.relatedurl | http://link.springer.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50291 | |
| dc.issue.number | 3 | |
| dc.journal.title | Statistical Papers | |
| dc.language.iso | eng | |
| dc.page.final | 366 | |
| dc.page.initial | 349 | |
| dc.publisher | Springer Verlag | |
| dc.relation.projectID | DGI BFM 2000-0800. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 519.22 | |
| dc.subject.keyword | K-phi-divergence | |
| dc.subject.keyword | goodness-of-fit | |
| dc.subject.keyword | second order limit distribution. | |
| dc.subject.ucm | Estadística matemática (Matemáticas) | |
| dc.subject.unesco | 1209 Estadística | |
| dc.title | Asymptotic approximations for the distributions of the K phi-divergence goodness-of-fit statistics | |
| dc.type | journal article | |
| dc.volume.number | 44 | |
| dcterms.references | Ali, S.M. and Silvey, S.D. (1966). A general class of coefficients of divergence of one distribution from another. Journal of the Royal Statistical Society Series B 28, 131-142. Burbea, J. and Rao, C.R. (1982). On the convexity of some divergence measures based on entropy functions. IEEE Transactions on Information Theory 28, 489-495. Cressie, N., and Read, T.R.C. (1984). Multinomial Goodness-of-fit Tests. Journal of the Royal Statistical Society Series B 46, 440-464. Csiszar, I. (1967). Information-type measures of difference of probability distributions and indirect observations. Studia Sci. Math. Hungar, 2, 299-318. Gvanceladze, L.G. and Chibisov, D.M. (1979). On tests of fit based on grouped data. In contributions to Statistics, J. Hajek Memorial Volume (editor J. JureDkova), 79-89. Prague, Academia. Mann, H.B., and Wald, A. (1942). On the choice of the number of class intervals in the application of the chi-square test. Annals ofMathematical Statistics 13, 306-317. Menendez, M.L., Morales, D., Pardo, L. and Salicri, M. (1992). Asymptotic distribution of the generalized distance measure in a random sampling. Proceeding of the International Meeting on Distance Analysis, DISTANCE'92, Remmes, France, 337-340. Menendez, M.L., Pardo, J.A., Pardo, L. and Pardo, M.C. (1997). Asymptotic approximations for the distribution of the (h,o}divergence goodness-of-fit statistic: Application to Renyi's statistic. Kibernetes, 26(4), 442-452. Morales, D., Pardo, L., Salicru, M. and Menendez, M.L. (1994). Asymptotic properties of divergence statistics in a stratified random sampling and its applications to test statistical hypotheses. Journal of Statistical Planning and Inference, 38, 2, 201-224. Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that can be reasonably supposed to have arisen from random sampling. Philosophy Magazine 50, 157-172. Perez and Pardo (1999). The Kb-divergence statistics for categorical data problem. Submitted. Ranga Rao, R. (1961). Some problems in probability theory. Ph. D. dissertation, Calcutta University. Abstract in Bull. Amer. Math. Soc. 67, 359-361. Read, T.R.C., and Cressie, N.A.C. (1988) Goodness of fit Statistics for discrete multivariate data. Springer-Verlag. Renyi, A. (1961). On measures of entropy and information. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability 1, 547-561. Schorr, B. (1974). On the choice of the class intervals in the application of the chi-squared test. Math. Operations forsch. Statist., 5, 357-377. Sharma, B.D. and Mittal, D.P. (1975) New Non-additive measures of relative information. Journal of Combinatory Information Systems Science, 2, 122-133. Sinha, B.K. (1976). On unbiasedness of Mann-Wald-Gumbell c2 test. Sankhya Series A 38,124-130. Siotani, M. and Fujikoshi, Y. (1984). Asymptotic approximations for the distributions of multinomial goodness-of-fit tests. Hiroshima Mathematics Journal 14, 115-124. Spruill, M.C. (1977). Equally Likely Intervals in the Chi-Square Test. Sankhya, Ser A, 39, 299-302. Yarnold, J.K. (1972). Asymptotic approximations for the probability that a sum of lattice random vectors lies in a convex set. Annals ofMathematical Statistics 43, 1566-1580. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 5e051d08-2974-4236-9c25-5e14369a7b61 | |
| relation.isAuthorOfPublication.latestForDiscovery | 5e051d08-2974-4236-9c25-5e14369a7b61 |
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