scholarly journals U-Statistic for Multivariate Stable Distributions

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Mahdi Teimouri ◽  
Saeid Rezakhah ◽  
Adel Mohammadpour
Keyword(s):  
Asymptotic Normality ◽  
Random Vector ◽  
Spectral Measure ◽  
Stable Distributions ◽  
Tail Index ◽  
Univariate Case ◽  
Stable Random Vector

A U-statistic for the tail index of a multivariate stable random vector is given as an extension of the univariate case introduced by Fan (2006). Asymptotic normality and consistency of the proposed U-statistic for the tail index are proved theoretically. The proposed estimator is used to estimate the spectral measure. The performance of both introduced tail index and spectral measure estimators is compared with the known estimators by comprehensive simulations and real datasets.

On estimating the tail index and the spectral measure of multivariate $$\alpha $$ α -stable distributions

Metrika ◽  
2014 ◽  
Vol 78 (5) ◽  
pp. 549-561 ◽  
Author(s):  
Mohammad Mohammadi ◽  
Adel Mohammadpour ◽  
Hiroaki Ogata
Keyword(s):  
Spectral Measure ◽  
Stable Distributions ◽  
Tail Index

scholarly journals A formula for hidden regular variation behavior for symmetric stable distributions

Extremes ◽  
2020 ◽  
Vol 23 (4) ◽  
pp. 667-691
Author(s):  
Malin Palö Forsström ◽  
Jeffrey E. Steif
Keyword(s):  
Power Law ◽  
Spectral Measure ◽  
Regular Variation ◽  
Stable Distributions ◽  
Decay Rates ◽  
Random Vectors ◽  
Power Law Decay ◽  
Exact Power ◽  
Hidden Regular Variation ◽  
Stable Random Vectors

Abstract We develop a formula for the power-law decay of various sets for symmetric stable random vectors in terms of how many vectors from the support of the corresponding spectral measure are needed to enter the set. One sees different decay rates in “different directions”, illustrating the phenomenon of hidden regular variation. We give several examples and obtain quite varied behavior, including sets which do not have exact power-law decay.

Asymptotic normality of location invariant heavy tail index estimator

Extremes ◽  
2009 ◽  
Vol 13 (3) ◽  
pp. 269-290 ◽  
Author(s):  
Jiaona Li ◽  
Zuoxiang Peng ◽  
Saralees Nadarajah
Keyword(s):  
Asymptotic Normality ◽  
Heavy Tail ◽  
Tail Index

scholarly journals A Peccati-Tudor type theorem for Rademacher chaoses

2019 ◽  
Vol 23 ◽  
pp. 874-892 ◽  
Author(s):  
Guangqu Zheng
Keyword(s):  
Random Vector ◽  
Type Theorem ◽  
Gaussian Vector ◽  
Univariate Case ◽  
Exchangeable Pairs ◽  
Chaos Decomposition ◽  
Main Strategy

In this article, we prove that in the Rademacher setting, a random vector with chaotic components is close in distribution to a centered Gaussian vector, if both the maximal influence of the associated kernel and the fourth cumulant of each component is small. In particular, we recover the univariate case recently established in Döbler and Krokowski (2019). Our main strategy consists in a novel adaption of the exchangeable pairs couplings initiated in Nourdin and Zheng (2017), as well as its combination with estimates via chaos decomposition.

scholarly journals LEVY-STABLE DISTRIBUTIONS REVISITED: TAIL INDEX > 2 DOES NOT EXCLUDE THE LEVY-STABLE REGIME

2001 ◽  
Vol 12 (02) ◽  
pp. 209-223 ◽  
Author(s):  
RAFAŁ WERON
Keyword(s):  
Stable Distribution ◽  
Stable Distributions ◽  
Tail Index ◽  
Fat Tails ◽  
Stable Regime ◽  
Finite Samples ◽  
Frequent Use ◽  
Financial Asset Returns ◽  
Index 2 ◽  
Log Linear

Power-law tail behavior and the summation scheme of Levy-stable distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset returns exhibit tail exponents well above the Levy-stable regime (0 < α ≤ 2). In this paper, we illustrate that widely used tail index estimates (log–log linear regression and Hill) can give exponents well above the asymptotic limit for α close to 2, resulting in overestimation of the tail exponent in finite samples. The reported value of the tail exponent α around 3 may very well indicate a Levy-stable distribution with α ≈ 1.8.

Asymptotic normality of processes with a branching structure

1998 ◽  
Vol 14 (4) ◽  
pp. 833-848
Author(s):  
Malcolm P. Quine ◽  
Władysław Szczotka
Keyword(s):  
Asymptotic Normality
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