Results 41 to 50 of about 1,203 (134)
International Journal of Stochastic Analysis, Volume 13, Issue 3, Page 261-267, 2000., 2000 Let X1, …, Xn be negatively dependent uniformly bounded random variables with d.f. F(x). In this paper we obtain bounds for the probabilities P(|∑i=1nXi|≥nt) and P(|ξˆpn−ξp|>ϵ) where ξˆpn is the sample pth quantile and ξp is the pth quantile of F(x). Moreover, we show that ξˆpn is a strongly consistent estimator of ξp under mild restrictions on F(x) in
M. Amini, A. Bozorgnia
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A strong law of large numbers for capacities
, 2005 We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the lower and the upper Choquet integrals of the random ...
Maccheroni, Fabio, Marinacci, Massimo
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A Durbin-Watson serial correlation test for ARX processes via excited adaptive tracking [PDF]
, 2014 We propose a new statistical test for the residual autocorrelation in ARX adaptive tracking. The introduction of a persistent excitation in the adaptive tracking control allows us to build a bilateral statistical test based on the well-known Durbin ...
Bercu, Bernard +2 more
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International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 171-177, 1999., 1999 Let {Xij} be a double sequence of pairwise independent random variables. If P{|Xmn| ≥ t} ≤ P{|X| ≥ t} for all nonnegative real numbers t and , for 1 < p < 2, then we prove that Under the weak condition of E|X|plog+|X| < ∞, it converges to 0 in L1. And the results can be generalized to an r‐dimensional array of random variables under the conditions ...
Dug Hun Hong, Seok Yoon Hwang
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On complete convergence for randomly indexed sums for a case without identical distributions
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 773-782, 1997., 1996 In this note we extend the complete convergence for randomly indexed sums given by Klesov (1989) to nonidentical distributed random variables.
Anna Kuczmaszewska, Dominik Szynal
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, 2012 Let X, X1, X2,... be a sequence of independent and identically distributed random variables in the domain of attraction of a normal distribution. A universal result in almost sure limit theorem for the self-normalized partial sums Sn/Vnis established ...
Qunying Wu
semanticscholar +1 more source
Complete convergence for weighted sums of arrays of rowwise ρ˜-mixing random variables
Journal of Inequalities and Applications, 2013 Let {Xni,i≥1,n≥1} be an array of rowwise ρ˜-mixing random variables. Some sufficient conditions for complete convergence for weighted sums of arrays of rowwise ρ˜-mixing random variables are presented without assumptions of identical distribution.
A. Shen, R. Wu, Xinghui Wang, Yan Shen
semanticscholar +1 more source
International Journal of Stochastic Analysis, Volume 10, Issue 1, Page 3-20, 1997., 1996 We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic for a class of strongly mixing sequences of random variables {Xi, i ≥ 1}. Stationarity is not assumed. Here is the perturbed empirical distribution function and Un is a U‐statistic based on X1, …, Xn.
Shan Sun, Ching-Yuan Chiang
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Higher-order expansions of powered extremes of normal samples
, 2016 In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants.
Ling, Chengxiu, Zhou, Wei
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On complete convergence of the sum of a random number of a stable type P random elements
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 1, Page 33-36, 1995., 1993 Complete convergence for randomly indexed normalized sums of random elements of the form is established. The random elements {Xn} belong to a type p stable space and are assumed to be independent, but not necessarily identically distributed. No assumptions are placed on the joint distributions of the stopping times {Tn}.
André Adler, Andrey Volodin
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