Limiting behavior of the perturbed empirical distribution functions evaluated at -statistics for strongly mixing sequences of random variables.
Sun, Shan, Chiang, Ching-Yuan (1997)
Journal of Applied Mathematics and Stochastic Analysis
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Displaying similar documents to “The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in ”
Limiting behavior of the perturbed empirical distribution functions evaluated at -statistics for strongly mixing sequences of random variables.
Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences
Jérôme Dedecker, Sana Louhichi (2005)
ESAIM: Probability and Statistics
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We continue the investigation started in a previous paper, on weak convergence to infinitely divisible distributions with finite variance. In the present paper, we study this problem for some weakly dependent random variables, including in particular associated sequences. We obtain minimal conditions expressed in terms of individual random variables. As in the i.i.d. case, we describe the convergence to the gaussian and the purely non-gaussian parts of the infinitely divisible limit....
Generalized covariance inequalities
Przemysław Matuła, Maciej Ziemba (2011)
Open Mathematics
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We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.
Central limit theorem of the smoothed empirical distribution functions for asymptotically stationary absolutely regular stochastic processes.
Elharfaoui, Echarif, Harel, Michel (2008)
Journal of Applied Mathematics and Stochastic Analysis
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Expected values in the alternative set theory and their applications to some limit theorems
Martin Kalina (1994)
Commentationes Mathematicae Universitatis Carolinae
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This article presents an alternative approach to statistical moments within non-standard models and by the help of these moments some limit theorems are reformulated and proved.
Exponential inequalities and functional central limit theorems for random fields
Jérôme Dedecker (2001)
ESAIM: Probability and Statistics
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We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform -mixing random fields, we require both finite fourth moments and an algebraic decay of the...