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The asymptotic behavior of linear placement statistics

Authors:	Dongjae Kim Wensheng Wang

Institution:	^a Department of Biostatistics, The Catholic University of Korea, Seoul, 137-701, Republic of Korea ^b Department of Mathematics, Yonsei University, Seoul, 120-749, Republic of Korea ^c School of Finance and Statistics, East China Normal University, Shanghai 200241, China

Abstract:	Orban and Wolfe (1982) and Kim (1999) provided the limiting distribution for linear placement statistics under null hypotheses only when one of the sample sizes goes to infinity. In this paper we prove the asymptotic normality and the weak convergence of the linear placement statistics of Orban and Wolfe (1982) and Kim (1999) when the sample sizes of each group go to infinity simultaneously.

Keywords:	primary 60F05 62E20 62G20 secondary 60E05 60E10
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