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Maximal inequalities for U-processes of strongly mixing random variables

Sancetta A.

Probability and Mathematical Statistics

2009

Vol. 29, Fasc. 1

155--167

Maximal inequalities for U-processes are required in order to achieve a reduction to the first nonvanishing term in their Hoeffding’s decomposition, which is the relevant quantity for statistical inference. This paper proves new maximal inequalities under strong mixing for U-processes in some function spaces. As an application we derive a uniform central limit theorem.

Strong laws of large numbers for random permanents

Rempała G. A., Wesołowski J.

Probability and Mathematical Statistics

2002

Vol. 22, Fasc. 2

201--209

The strong laws of large numbers for random permanents of increasing order are derived. The method of proofs relies on the martingale decomposition of a random permanent function similar to the one known for U-statistics.