Asymptotic linearity of a linear rank statistic in the case of symmetric nonidentically distributed variables

Abstract

Let Y 1, ...., Y n be independent but not identically distributed random variables with densities f 1, ...., f n symmetric around zero. Suppose c 1, n , ...., c n, n are given constants such that ? i c i, n =0 and . Denote the rank of Y i -? c i, n for any ??R by R(Y i -? c i, n ) and let a n (i) be a score defined via a score function ?. We study the linear rank statistic and prove that S n (?) is asymptotically uniformly linear in the parameter ? in any interval [-C, C], C>0.

Keywords

linear rank statistic; Hajek projection of rank statistics; contiguity; linear rank regression; nonidentically distributed errors

Published in

Statistics
2013, Volume: 47, number: 1, pages: 156-171 Publisher: TAYLOR & FRANCIS LTD

SLU Authors

• Kuljus, Kristi

  • Department of Forest Economics, Swedish University of Agricultural Sciences
    

UKÄ Subject classification

Probability Theory and Statistics


Publication identifier

DOI: https://doi.org/10.1080/02331888.2011.568116

Permanent link to this page (URI)

https://res.slu.se/id/publ/56177