UNIVERSITY
OF WROCŁAW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.2 43.1 42.2 42.1 41.2 41.1 40.2
40.1 39.2 39.1 38.2 38.1 37.2 37.1
36.2 36.1 35.2 35.1 34.2 34.1 33.2
33.1 32.2 32.1 31.2 31.1 30.2 30.1
29.2 29.1 28.2 28.1 27.2 27.1 26.2
26.1 25.2 25.1 24.2 24.1 23.2 23.1
22.2 22.1 21.2 21.1 20.2 20.1 19.2
19.1 18.2 18.1 17.2 17.1 16.2 16.1
15 14.2 14.1 13.2 13.1 12.2 12.1
11.2 11.1 10.2 10.1 9.2 9.1 8
7.2 7.1 6.2 6.1 5.2 5.1 4.2
4.1 3.2 3.1 2.2 2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 21, Fasc. 2,
pages 277 - 302
 

EDGEWORTH EXPANSIONS FOR L -STATISTICS

Ivo B. Alberink
Gyula Pap
Martien C. A. van Zuijlen

Abstract: We study the approximation by a short Edgeworth expansion of the distribution function of normalized linear combinations

1 sum n V~ -- cjnXj:n n j=1
of order statistics of n independent random variables with common distribution function F. Under the assumptions
|cjn| < Cn-p1 [j -- n(1 -j- 1 ----- n)]-p2 ,
|cjn - cj-1,n| < Cn-q1 [j -- n(1 -j- 1 ----- n)]-q2 ,
|cj+1,n - 2cjn + cj-1,n| < Cn-r1 [j -- n(1 -j- 1 ----- n)]-r2 ,
(F-1)'(s) < C[s(1 - s)]-k
for some p1,q1,r1 (- R, p2,q2,r2,C > 0, k (- [0,5/4), with an appropriate balance in these parameters, and under additional moment conditions, the rate of uniform convergence is shown to be of order n-1. Moreover, a special case is considered where the cjn are generated by a sequence of weight functions of a special structure.

1991 AMS Mathematics Subject Classification: 62E20.

Key words and phrases: Linear combinations of order statistics, Edgeworth expansions, rate of convergence.

Download:    Abstract    Full text   Abstract + References