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Article Dans Une Revue Mathematical Methods of Statistics Année : 2013

A strong large deviation theorem

Résumé

We prove a strong large deviation theorem for an arbitrary sequence of random variables, that is, we establish a full asymptotic expansion of large deviation type for the tail probabilities. An Edgeworth expansion is required to derive the result. We illustrate our theorem with two statistical applications : the sample variance and the kernel density estimator.
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Dates et versions

hal-00821719 , version 1 (12-05-2013)

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Cyrille Joutard. A strong large deviation theorem. Mathematical Methods of Statistics, 2013, 22 (2), pp.155-164. ⟨10.3103/S1066530713020051⟩. ⟨hal-00821719⟩
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