Some asymptotic properties of the hybrids of empirical and partial-sum processes. (English) Zbl 1143.60326

Summary: The motivation of this paper is to study some properties of the local times (when it exists) of the hybrids of empirical and partial-sum processes defined by \[ \bar{A}_n(t)=\sum _{1\leq i \leq n} H(X_i)1_{\{X_i\leq t\}} \epsilon_i, - \infty < t < \infty , \] namely by using knowing results on empirical process and Brownian local times.


60J55 Local time and additive functionals
60F15 Strong limit theorems
60F17 Functional limit theorems; invariance principles
62G30 Order statistics; empirical distribution functions
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