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Weak convergence of the weighted empirical quantile process in \(L^ 2(0,1)\). (English) Zbl 0543.60010

The author considers the weighted empirical quantile process as a random element in \(L^ 2(0,1)\) and finds conditions under which the empirical quantile process converges in distribution to a weighted Brownian bridge. Then the obtained conditions are applied to the derivation of the asymptotic distribution of goodness of fit tests based on sample quantiles that can be written as continuous functionals defined on \(L^ 2(0,1)\).
Reviewer: S.A.Chobanjan

MSC:

60B10 Convergence of probability measures
62G10 Nonparametric hypothesis testing
60F05 Central limit and other weak theorems
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