Distance between exact and approximate distributions of partial maxima under power normalization
Volume 2, Issue 4 (2015), pp. 391–399
Pub. online: 23 December 2015
Type: Research Article
Open Access
Open Access
1
Research work supported by Post Doctoral Fellowship for Women of the University Grants Commission (UGC), New Delhi. Ref: No.F. 15-1/2011-12/PDFWM-2011-12-GE-KAR-2333(SA-II) dated 1 Nov 2013.
2
Research work supported by UGC Major Research Project F.No. 43-541/2014(SR) dated 16.10.2015
Received
7 October 2015
7 October 2015
Revised
4 December 2015
4 December 2015
Accepted
4 December 2015
4 December 2015
Published
23 December 2015
23 December 2015
Abstract
We obtain the distance between the exact and approximate distributions of partial maxima of a random sample under power normalization. It is observed that the Hellinger distance and variational distance between the exact and approximate distributions of partial maxima under power normalization is the same as the corresponding distances under linear normalization.
References
Cormann, U., Reiss, R.-D.: Generalizing the Pareto to the log-Pareto model and statistical inference. Extremes 12(1), 93–105 (2009). MR2480725. doi:10.1007/s10687-008-0070-6
Falk, M., Hüsler, J., Reiss, R.-D.: Laws of Small Numbers: Extremes and Rare Events. Springer (2010). MR2732365. doi:10.1007/978-3-0348-0009-9
Hellinger, E.: Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen. J. Reine Angew. Math. 136, 210–271 (1909). MR1580780. doi:10.1515/crll.1909.136.210
Mohan, N., Ravi, S.: Max domains of attraction of univariate and multivariate p-max stable laws. Theory Probab. Appl. 37(4), 632–643 (1993). MR1210055. doi:10.1137/1137119
Mohan, N., Subramanya, U.: On the convergence of the density of the power normalized maximum. Calcutta Stat. Assoc. Bull. 48(189-19), 13–20 (1998). MR1677401
Patra, R.K., Mandal, A., Basu, A.: Minimum Hellinger distance estimation with inlier modification. Sankhyā, Indian J. Stat. B (2008), 70(2), 310–322 (2008). MR2563992
Ravi, S., Praveena, A.S.: On von Mises type conditions for p-max stable laws, rates of convergence and generalized log Pareto distributions. J. Stat. Plan. Inference 141(9), 3021–3034 (2011). MR2796008. doi:10.1016/j.jspi.2011.03.024
Reiss, R.: Approximate Distributions of Order Statistics. With Applications to Nonparametric Statistics. Springer Series in Statistics. Springer (1989). MR0988164. doi:10.1007/978-1-4613-9620-8
