A necessary test of fit of specific elliptical distributions based on an estimator of Song's measure
Φόρτωση...
Ημερομηνία
Συγγραφείς
Batsidis, A.
Zografos, K.
Τίτλος Εφημερίδας
Περιοδικό ISSN
Τίτλος τόμου
Εκδότης
Elsevier
Περίληψη
Τύπος
Είδος δημοσίευσης σε συνέδριο
Είδος περιοδικού
peer reviewed
Είδος εκπαιδευτικού υλικού
Όνομα συνεδρίου
Όνομα περιοδικού
Journal of Multivariate Analysis
Όνομα βιβλίου
Σειρά βιβλίου
Έκδοση βιβλίου
Συμπληρωματικός/δευτερεύων τίτλος
Περιγραφή
In a recent paper, Zografos [K. Zografos, On Mardia's and Song's measures of kurtosis in elliptical distributions, J. Multivariate Anal. 99 (2008) 858-879] has obtained general formulas for Song's measure for the elliptic family of distributions, and he introduced and studied its sample analogue. In this paper, based on the empirical estimator of this measure, we present a test to verify if the data are distributed according to a specific elliptical (spherical) distribution. In this context, the asymptotic distribution of the proposed statistic under the null hypothesis of specific spherical distributions is obtained. The proposed statistic also provides us with a procedure for testing multivariate normality. In order to evaluate the convergence of the proposed statistic to its limiting distribution, under the null hypothesis, a simulation study is performed to analyze the behavior of the percentiles of the proposed statistic in some special cases of spherical distributions. Moreover, a Monte Carlo study is carried out on the performance of the test statistic as a necessary test of fit of specific spherical distributions. In this framework, the type I error rates as well as the power of the test are studied. Finally, a well-known data set is used to illustrate the method developed in this paper. (C) 2011 Elsevier Inc. All rights reserved.
Περιγραφή
Λέξεις-κλειδιά
song's measure, multivariate normality, monte carlo study, elliptic distributions, ellipsoidal symmetry, multivariate, skewness, kurtosis, normality
Θεματική κατηγορία
Παραπομπή
Σύνδεσμος
<Go to ISI>://000310865300009
http://ac.els-cdn.com/S0047259X11001941/1-s2.0-S0047259X11001941-main.pdf?_tid=db6fc308-c8fa-11e2-8c30-00000aab0f27&acdnat=1369899232_cd462a09e0d0a8f581d9c9288f74e745
http://ac.els-cdn.com/S0047259X11001941/1-s2.0-S0047259X11001941-main.pdf?_tid=db6fc308-c8fa-11e2-8c30-00000aab0f27&acdnat=1369899232_cd462a09e0d0a8f581d9c9288f74e745
Γλώσσα
en
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Όνομα επιβλέποντος
Εξεταστική επιτροπή
Γενική Περιγραφή / Σχόλια
Ίδρυμα και Σχολή/Τμήμα του υποβάλλοντος
Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών