Bounds on moments of symmetric statistics

2002 ◽  
Vol 39 (3-4) ◽  
pp. 251-275 ◽  
Author(s):  
R. Ibragimov ◽  
Sh. Sharakhmetov
Keyword(s):  
Arbitrary Order ◽  
Random Variables ◽  
Best Constants ◽  
Moment Inequalities ◽  
Rate Of Growth ◽  
Symmetric Statistics

In this paper we prove analogues of Khintchine, Marcinkiewicz-Zygmund and Rosenthal moment inequalities for symmetric statistics of arbitrary order in not identically distributed random variables. We also construct an example that shows the significance of each term in the obtained Rosenthal-type inequalities for symmetric statistics and obtain results concerning the rate of growth of the best constants in the inequalities.

A Poisson limit theorem for incomplete symmetric statistics

1983 ◽  
Vol 20 (01) ◽  
pp. 47-60 ◽  
Author(s):  
M. Berman ◽  
G. K. Eagleson
Keyword(s):  
Limit Theorem ◽  
Limit Theorems ◽  
Random Variables ◽  
Asymptotic Distributions ◽  
Poisson Limit ◽  
Symmetric Statistics ◽  
Limit Result ◽  
Independent Identically Distributed

Silverman and Brown (1978) have derived Poisson limit theorems for certain sequences of symmetric statistics, based on a sample of independent identically distributed random variables. In this paper an incomplete version of these statistics is considered and a Poisson limit result shown to hold. The powers of some tests based on the incomplete statistic are investigated and the main results of the paper are used to simplify the derivations of the asymptotic distributions of some statistics previously published in the literature.

Moment inequalities for positive random variables

2010 ◽  
Vol 348 (11-12) ◽  
pp. 687-690 ◽  
Author(s):  
Christopher S. Withers ◽  
Saralees Nadarajah
Keyword(s):  
Random Variables ◽  
Moment Inequalities

Moving-average models with bivariate exponential and geometric distributions

1987 ◽  
Vol 24 (01) ◽  
pp. 48-61
Author(s):  
Naftali A. Langberg ◽  
David S. Stoffer
Keyword(s):  
Moving Average ◽  
Random Variables ◽  
Moment Inequalities ◽  
Random Vectors ◽  
Positive Dependence ◽  
Associated Random Variables ◽  
Bivariate Exponential ◽  
Moving Average Models ◽  
Joint Probabilities

Two classes of finite and infinite moving-average sequences of bivariate random vectors are considered. The first class has bivariate exponential marginals while the second class has bivariate geometric marginals. The theory of positive dependence is used to show that in various cases the two classes consist of associated random variables. Association is then applied to establish moment inequalities and to obtain approximations to some joint probabilities of the bivariate processes.

scholarly journals Φ-moment inequalities for independent and freely independent random variables

2016 ◽  
Vol 270 (12) ◽  
pp. 4558-4596 ◽  
Author(s):  
Yong Jiao ◽  
Fedor Sukochev ◽  
Guangheng Xie ◽  
Dmitriy Zanin
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Moment Inequalities

scholarly journals On the rate of growth of norming multiple and the upper and lower functions of the sum of independent random variables

1970 ◽  
Vol 10 (1) ◽  
pp. 61-68
Author(s):  
N. Kalinauskaitė
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Rate Of Growth ◽  
Upper And Lower Functions

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Н. Калинаускайте. О скорости роста нормирующего множителя и верхних и нижних функциях для сумм независимых случайных величин N. Kalinauskaitė. Viršutinių ir apatinių funkcijų nepriklausomų dydžių sumoms ir normuojančio daugiklio greičio klausimu

Sign in / Sign up

Export Citation Format

Share Document