 Asymptotic normality of winsorized meansPhilip S. Griffin Stochastic Processes and their Applications, 1988, vol. 29, issue 1, 107-127 Abstract: Let Xi be non-degenerate i.i.d. random variables with distribution function F, and let Xn1,...,Xnn denote the order statistics of X1,...,Xn. In trying to robustify the sample mean as an estimator of location, several alternatives have been suggested which have the intuitive appeal of being less susceptible to outliers. Here the asymptotic distribution of one of these, the Winsorized mean, which is given by where rn[greater-or-equal, slanted]0, sn[greater-or-equal, slanted]0 and rn+sn[greater-or-equal, slanted]n, is studied. The main results include a necessary and sufficient condition for asymptotic normality of the Winsorized mean under the assumption that rn-->[infinity], sn-->[infinity], rnn-1-->0, snn-1-->0 and F is convex at infinity. It is also shown, perhaps somewhat surprisingly, that if the convexity assumption on F is dropped then the Winsorized mean may fail to be asymptotically normal even when X1 is bounded! Keywords: Winsorized; mean; robustified; mean; asymptotic; behaviour; convexity; condition (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:29:y:1988:i:1:p:107-127 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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