A preliminary test in classification and probabilities of misclassification
| dc.contributor.author | Menéndez, María Luisa | |
| dc.contributor.author | Pardo Llorente, Julio Ángel | |
| dc.contributor.author | Pardo Llorente, Leandro | |
| dc.contributor.author | Zografos, Konstantinos | |
| dc.date.accessioned | 2023-06-20T09:43:12Z | |
| dc.date.available | 2023-06-20T09:43:12Z | |
| dc.date.issued | 2005-06 | |
| dc.description.abstract | Consider f(theta) to be a probability density function with parameter theta. A set of k populations can now be defined such that the ith population Pi(i) is the set of density functions f(theta 1(i)),...,f(theta mi(i)). This paper proposes a test, based on the Psi-dissimilariiy, of the hypothesis that a new individual from a population Pi(0) with a density function f(theta 0), belongs to the ith population. The probabilities of misclassification of the minimum Psi-dissimilarity classification rule are also obtained. In this paper, it is assumed that the parameters theta(1)((i)),...,theta(mi)((i)) and may be theta(0) are unknown and must be estimated from a set of training samples. Explicit expressions for the hypothesis test and the probabilities of misclassification are derived for the case where the populations Pi(i) consist of homoscedastic normal, as well as for gamma distributions. | |
| dc.description.department | Depto. de Estadística e Investigación Operativa | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio Griego para el Desarrollo. | |
| dc.description.sponsorship | Ministerio Español de Asuntos Exteriores | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17495 | |
| dc.identifier.doi | 10.1080/02331880500097986 | |
| dc.identifier.issn | 0233-1888 | |
| dc.identifier.officialurl | http://www.tandfonline.com/doi/pdf/10.1080/02331880500097986 | |
| dc.identifier.relatedurl | http://www.tandfonline.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50243 | |
| dc.issue.number | 3 | |
| dc.journal.title | Statistics | |
| dc.language.iso | eng | |
| dc.page.final | 205 | |
| dc.page.initial | 183 | |
| dc.publisher | Taylor & Francis | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 519.237 | |
| dc.subject.keyword | Classification | |
| dc.subject.keyword | Discrimination | |
| dc.subject.keyword | Minimum distance classification rule | |
| dc.subject.keyword | Probabilities of misclassification | |
| dc.subject.keyword | ϕ-Dissimilarity | |
| dc.subject.keyword | φ-Divergence | |
| dc.subject.ucm | Estadística matemática (Matemáticas) | |
| dc.subject.unesco | 1209 Estadística | |
| dc.title | A preliminary test in classification and probabilities of misclassification | |
| dc.type | journal article | |
| dc.volume.number | 39 | |
| dcterms.references | Krzanowski, W.J., 1988, Principles of Multivariate Analysis. A User’s Perspective (Oxford: Oxford Science Publications). Matusita, K., 1966, A distance and related statistics in multivariate analysis. In: P.R. Krishnaiah (Ed.), Multivariate Analysis (NewYork: Academic Press), pp. 187–200. Matusita, K., 1967, On the notion of affinity of several distributions and some of its applications. Annals of the Institute of Statistical Mathmetics, 19, 181–192. McLachlan, G.J., 1992, Discriminant Analysis and Statistical Pattern Recognition (NewYork:Wiley). Cacoullos, T. and Koutras, M., 1985, Minimum distance discrimination for spherical distributions. In: K. Matusita (Ed.) Statistical Theory and Data Analysis (North-Holland: Elsevier Science Publishers B. V.), pp. 91–101. Cacoullos, T. andKoutras, M., 1997, On the performance of minimum-distance classification rules forKotz-type elliptical distributions. In: N.L. Johnson and N. Balakrishnan (Eds), Advances in the Theory and Practice of Statistics: a Volume in Honor of Samuel Kotz (NewYork:Wiley), pp. 209–224. Koutras, M., 1992, Minimum distance discrimination rules and success rates for elliptical normal mixtures. Statistics and Probability Letters, 13, 259–268. Csiszár, I., 1963, Eine informationstheoretische ungleichung und ihre anwendung auf den beweis der ergodizitat von Markoffschen Ketten. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 8, 85–108. 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-statistical, 28, 131–142. Koutras, M., 1987, On the performance of the linear discriminant function for spherical distributions. Journal of Multivariate Analysis, 22, 1–12. Bar-Hen, A., 1996, A preliminary test in discriminant analysis. Journal of Multivariate Analysis, 57, 266–276. Kala, R. and Krzy´sko, M., 2003, An extension of Bar-Hen’s preliminary test procedure. Journal of Multivariate Analysis, 84, 410–412. Bar-Hen, A. and Daudin, J.J., 1997, A test of a special case of typicality in linear discriminant analysis. Biometrics, 53, 39–48. Gyorfi, L. and Nemetz, T., 1978, f -Dissimilarity: a generalization of the affinity of several distributions. Annals of the Institute of Statistical Mathematics, 30, 105–113. Zografos, K., 1998, f -Dissimilarity of several distributions in testing statistical hypotheses. Annals of the Institute of Statistical Mathematics, 50, 295–310. Morales, D., Pardo, L. and Zografos, K., 1998, Informational distances and related statistics in mixed continuous and categorical variables. Journal of Statistical Planning and Inference, 75, 47–63. Serfling, R.J., 1980, Approximation Theorems of Mathematical Statistics (NewYork:Wiley). Bishop,Y.M.M., Fienberg, S.E. and Holland, P.W., 1975, Discrete Multivariate Analysis: Theory and Practice. (Cambridge: The M.I.T. Press). Toussaint, G.T., 1974, Some properties of Matusita’s measure of affinity of several distributions. Annals of the Institute of Statistical Mathematics, 26, 389–394. Vajda, I., 1989, Theory of Statistical Inference and Information (The Netherlands: KluwerAcademic Publishers). Menéndez, M.L., 2000, Shannon’s entropy in exponential families: statistical applications. Applied Mathematics Letters, 13, 37–42. Mayer-Wolf, E., 1990, The Cramer-Rao functional and limiting laws. Annals of Probability, 18, 840–850. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 5e051d08-2974-4236-9c25-5e14369a7b61 | |
| relation.isAuthorOfPublication | a6409cba-03ce-4c3b-af08-e673b7b2bf58 | |
| relation.isAuthorOfPublication.latestForDiscovery | 5e051d08-2974-4236-9c25-5e14369a7b61 |
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