A Gibbs Conditional theorem under extreme deviation

2016/10/13 by Maeva Biret, Michel Broniatowski, Biret, Maeva +3
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1610.04052

arXiv admin note: text overlap with arXiv:1206.6951, arXiv:1305.3482

arxiv created 2016/10/13 · arxiv updated 2016/10/14

Abstract

We explore some properties of the conditional distribution of an i.i.d. sample under large exceedances of its sum. Thresholds for the asymptotic independance of the summands are observed, in contrast with the classical case when the conditioning event is in the range of a large deviation. This paper is an extension to [7]. Tools include a new Edgeworth expansion adapted to specific triangular arrays where the rows are generated by tilted distribution with diverging parameters, together with some Abelian type results.

Citations

• A conditional limit theorem for random walks under extreme deviation
• Light tails: Gibbs conditional principle under extreme deviation

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