Weighted similarity tests for location-scale families of stable distributions. Issue 16 (17th August 2016)

• Record Type: Journal Article
• Authors: Dorea, Chang C. Y.; Lopes, Luciene P.
• Is Part Of: Communications in statistics. Volume 45:Issue 16(2016)
• Page Start: 4912
• Page End: 4922
• Publication Date: 2016-08-17
• Subjects: Mallows distance -- Similarity test -- Stable distribution -- Weighted distribution.; 62F05 -- 60E07 -- 60F05.; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.932809
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: The class of stable distributions plays a central role in the study of asymptotic behavior of normalized partial sums, the same role performed by normal distribution among those with finite second moment. In this note, by exploiting the connection between stable laws and regularly varying functions, we present weighted similarity tests for stable location-scale families. The proposed weight functions are based on the 2nd-order Mallows distance between the empirical distribution and the root stable distribution. And the resulting statistics converge weakly to functionals of Brownian bridge.