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Displaying similar documents to “Conditional moment representations for dependent random variables.”

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 φ -mixing random fields, we require both finite fourth moments and an algebraic decay of the...

The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in 𝕃 p

Jérôme Dedecker, Florence Merlevède (2007)

ESAIM: Probability and Statistics

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Considering the centered empirical distribution function as a variable in 𝕃 p ( μ ) , we derive non asymptotic upper bounds for the deviation of the 𝕃 p ( μ ) -norms of as well as central limit theorems for the empirical process indexed by the elements of generalized Sobolev balls. These results are valid for a large class of dependent sequences, including non-mixing processes and some dynamical systems.

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.