Estimation améliorée explicite d'un degré de confiance conditionnel

Abstract

We consider the problem of estimating the confidence statement of the usual confidence set, with confidence coefficient 1− α, of the mean of a p-variate normal distribution with identity covariance matrix. For p⩾5, we give an explicit sufficient condition for domination over the standard estimator 1− α by an estimator correcting it, that is, by 1− α+ s where s is a suitable function. That condition mainly relies on a partial differential inequality of the form kΔ s+ s 2⩽0 (for a certain constant k>0). It allows us to formally establish (with no recourse to simulations) this domination result. To cite this article: D. Fourdrinier, P. Lepelletier, C. R. Acad. Sci. Paris, Ser. I 337 (2003).