On the Asymptotic Behavior of Sums of Order Statistics from a Distribution with a Slowly Varying Upper Tail
Let (X n)n≥1 be a sequence of independent non-negative random variables from a common distribution function F with a regiilarly varying upper tail. A number of results are presented on the stability, asymptotic distribution and law of the iterated logarithm for trimmed sums formed by deleting a number of the upper extreme values from the partial sum X 1 +...+X n at each stage n. The methods of proof are entirely based on quantile function techniques. This paper should provide the reader with a good introduction to some of the possibilities and the scope of this methodology.
KeywordsAsymptotic Distribution Empirical Process Iterate Logarithm Empirical Distribution Function Common Distribution Function
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- HAAN, DE, L. (1975). On Regular Variation and Its Application to the Weak Convergence of Sample Extremes. Mathematical Centre Tracts 32, Amsterdam.Google Scholar
- KIEFER, J. (1972). Iterated logarithm analogues for sample quantities when Pn ↓ 0. Proc. Sixth Berkeley Symp. Math. Statist. Prohab. Vol. I, 227–244.Google Scholar
- MORI, T. (1981). The relation of sums and extremes of random variables. Session Summary Booklet, Invited Papers, Buenos Aires Session, Nov. 30-Dec. 11, (International Statistical Institute) 879–894.Google Scholar
- SHORACK, G.R. and WELLNER, J.A. (1986). Empirical Processes with Application to Statistics. Wiley, New York.Google Scholar