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

作者：Kuljus Kristi^*; Zwanzig Silvelyn

来源：Statistics, 2013, 47(1): 156-171.

DOI：10.1080/02331888.2011.568116

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

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%26gt;0.

• 出版日期2013-2-1