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The asymptotic distribution of magnitude-Winsorized sums via self-normalization (1990)

Hahn, Marjorie G. ; Kuelbs, Jim ; Weiner, Daniel C.

Springer

Journal of theoretical probability 3 (1990), S. 137-168

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ISSN: 1572-9230

Keywords: Winsorized sums ; self-normalization ; trimmed sums ; magnitude order statistics ; asymptotic normality ; variance-mixtures of normals ; stochastic compactness ; weak convergence ; universal law

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Asymptotic normality, tightness, and weak convergence of the magnitude-Winsorized sums formed from symmetric i.i.d. random variables are studied via a new approach that first derives self-normalized (“studentized”) results and then uses these to derive results for constant normalizations. An application of this method to trimmed sums is also discussed to demonstrate its more general applicability as well as to illustrate its use.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01063331

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