When does a randomly weighted self-normalized sum converge in distribution?
Mason, David M., Zinn, Joel (2005)
Electronic Communications in Probability [electronic only]
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Displaying similar documents to “Large and moderate deviations for Hotelling's -statistic.”
When does a randomly weighted self-normalized sum converge in distribution?
A tail inequality for suprema of unbounded empirical processes with applications to Markov chains.
Adamczak, Radoslaw (2008)
Electronic Journal of Probability [electronic only]
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Statistical tools for discovering pseudo-periodicities in biological sequences
Bernard Prum, Élisabeth de Turckheim, Martin Vingron (2001)
ESAIM: Probability and Statistics
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Many protein sequences present non trivial periodicities, such as cysteine signatures and leucine heptads. These known periodicities probably represent a small percentage of the total number of sequences periodic structures, and it is useful to have general tools to detect such sequences and their period in large databases of sequences. We compare three statistics adapted from those used in time series analysis: a generalisation of the simple autocovariance based on a similarity score...
Infinite system of Brownian balls with interaction: the non-reversible case
Myriam Fradon, Sylvie Rœlly (2007)
ESAIM: Probability and Statistics
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We consider an infinite system of hard balls in undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also show that Gibbs measures are reversible measures.
A tail bound for sums of independent random variables and application to the Pareto distribution.
Chesneau, Christophe (2009)
Applied Mathematics E-Notes [electronic only]
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On standard normal convergence of the multivariate Student -statistic for symmetric random vectors.
Giné, Evarist, Götze, Friedrich (2004)
Electronic Communications in Probability [electronic only]
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A bound on the deviation probability for sums of non-negative random variables.
Maurer, Andreas (2003)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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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....