Abstract
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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Joutard, C. A strong large deviation theorem. Math. Meth. Stat. 22, 155–164 (2013). https://doi.org/10.3103/S1066530713020051
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DOI: https://doi.org/10.3103/S1066530713020051