On the asymptotic distribution of weighted uniform empirical and quantile processes in the middle and on the tails

Miklós Csörgo and David M. Mason

Stochastic Processes and their Applications, 1985, vol. 21, issue 1, 119-132

Abstract: Let [alpha]n and un be the uniform empirical and quantile processes. We investigate the asymptotic distribution of the suprema of [alpha]n(s)/(s(1 - s))1/2±[nu] and un(s)/(s(1 - s))1/2±[nu] with , when the supremum is taken over ranges, depending on n, in the middle of the interval [0, 1], near 0 and near 1. We show that with suitable norming factors the said asymptotic distributions can be radically different or the same, depending on the sign and value of [nu] in the weight function 1/(s(1 - s))1/2±[nu].

Keywords: weighted; empirical; and; quantile; processes; asymptotic; distributions; approximations (search for similar items in EconPapers)
Date: 1985
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