Many authors have followed up the work of Hall, but complete asymptotic expansions have not been known for normal extremes. Here, we derive such expansions for the first time. The expansions are single infinite sums of terms involving Bell polynomials and Stirling numbers. The usefulness of the ...
that (i) sums of stationary and strong mixing sequences are asymptotically normal; further, (ii) these sums are asymptotically independent of the extrema of the sequences (Anderson and Turkman 1991; =-=Hsing 1995-=-). It will be instructive to determine how well our results support these ...
Asymptotic proper- ties of sums of upper records. Extremes, 6(2): 147-164.Bose, Arup; Gangopadhyay, Sreela; Sarkar, Anish and Sengupta, Arindam (2001). Asymp- totic properties of sums of upper records. Submitted for publication.A. Bose, S. Gangopadhyay, A. Sarkar and A. Sengupta, ...
M. Mason, On the asymptotic behavior of sums of order statistics from a distribution with a slowly varying upper tail, in Sums, Trimmed Sums and Extremes, M. G. Hahn, D. M. Mason, and D. C. Weiner, eds., Birkh¨auser, Boston, Basel, Berlin, 1991, pp. 355-376....
The same result holds for n even. 5.2 Extreme Order Statistics The situation is more complicated when p1=0 or pk=1, corresponding to the extremes X1:n, Xn:n and more generally to the mth extremes Xm:n, Xn+1−m:n, where m is a fixed positive integer. For Xn:n, suitably ...
(1991), Asymptotic behavior of partial sums: a more robust approach via trimming and self-normalization, Sum, trimmed sums and extremes, Progr. Probab., 23, 1-53.M.G. Hahn, J. Kuelbs and D.C. Weiner, Asymptotic behavior of partial sums: a more robust approach via trimming and self-...