Add to ORKGInternational audienceWe establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain. The constants in this inequality are explicit and depend on computable bounds on the mixing rate of the Markov Chain. We apply this result to derive the strong law of large number for U-statistics of a Markov Chain under conditions which are close from being optimal
Partial sums and sample means of r-dimensionally indexed arrays of independent random variables have...
We prove the central limit theorem for U-statistics whose underlying sequence of random variables sa...
International audienceWe prove concentration inequalities for some classes of Markov chains and Φ-mi...
International audienceWe establish a simple variance inequality for U-statistics whose underlying se...
International audienceWe prove a new concentration inequality for U-statistics of order two for unif...
The strong law of the large numbers for U-statistics has been proved for a sequence of independent r...
International audienceDespite the ubiquity of U-statistics in modern Probability and Statistics, the...
Strong laws of large numbers are given for L-statistics (linear combinations of order statistics) an...
In this work, we study the almost sure convergence of the averages of certain classes of sequences a...
Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work of researchers of th...
We develop explicit, general bounds for the probability that the empirical sample averages of a func...
Abstract. We introduce a new property of Markov chains, called variance bounding. We prove that, for...
We develop explicit, general bounds for the probability that the normalized partial sums of a functi...
AbstractIn the paper bounds are introduced for operators appearing when summing up random variables ...
Partial sums and sample means of r-dimensionally indexed arrays of independent random variables have...
We prove the central limit theorem for U-statistics whose underlying sequence of random variables sa...
International audienceWe prove concentration inequalities for some classes of Markov chains and Φ-mi...
International audienceWe establish a simple variance inequality for U-statistics whose underlying se...
International audienceWe prove a new concentration inequality for U-statistics of order two for unif...
The strong law of the large numbers for U-statistics has been proved for a sequence of independent r...
International audienceDespite the ubiquity of U-statistics in modern Probability and Statistics, the...
Strong laws of large numbers are given for L-statistics (linear combinations of order statistics) an...
In this work, we study the almost sure convergence of the averages of certain classes of sequences a...
Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work of researchers of th...
We develop explicit, general bounds for the probability that the empirical sample averages of a func...
Abstract. We introduce a new property of Markov chains, called variance bounding. We prove that, for...
We develop explicit, general bounds for the probability that the normalized partial sums of a functi...
AbstractIn the paper bounds are introduced for operators appearing when summing up random variables ...
Partial sums and sample means of r-dimensionally indexed arrays of independent random variables have...
We prove the central limit theorem for U-statistics whose underlying sequence of random variables sa...
International audienceWe prove concentration inequalities for some classes of Markov chains and Φ-mi...