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- W2017011636 abstract "SummaryOften, many complicated statistics used as estimators or test statistics take the form of the (multivariate) empirical distribution function evaluated at a random vector (Vn). Denote such statistics by Sn. This paper describes methods for the study of various asymptotic properties of Sn. First, under minimal assumptions, a weak asymptotic representation for Sn is derived. This result may be used to show the asymptotic normality of Sn. Second, under slightly more stringent regularity conditions, an almost sure representation of Sn, with suitable order (as.) of the remainder term is studied and then a law of the iterated logarithm for Sn, is derived. In this context, strong convergence results from a sequential point of view are also studied. Finally, weak convergence to a Brownian motion process is established. As an application, we show the limiting normality of Sn, for a random number of summands." @default.
- W2017011636 created "2016-06-24" @default.
- W2017011636 creator A5080347070 @default.
- W2017011636 date "1986-09-01" @default.
- W2017011636 modified "2023-09-23" @default.
- W2017011636 title "Asymptotic Representations of the Multivariate Empirical Distribution Function and Applications" @default.
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- W2017011636 doi "https://doi.org/10.1111/j.1467-842x.1986.tb00705.x" @default.
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