The asymptotic behavior of linear placement statistics. (English) Zbl 1236.62006
Summary: J. Orban and D.A. Wolfe [J. Am. Stat. Assoc. 77, 666–672 (1982; Zbl 0499.62038)]) and D. Kim [Far. East J. Theor. Stat. 3, 19–33 (1999)] provided the limiting distribution for linear placement statistics under null hypotheses only when one of the sample sizes goes to infinity. We prove the asymptotic normality and the weak convergence of the linear placement statistics of Orban and Wolfe and of Kim when the sample sizes of each group go to infinity simultaneously.
MSC:
| 62E20 | Asymptotic distribution theory in statistics |
| 60F05 | Central limit and other weak theorems |
| 62G20 | Asymptotic properties of nonparametric inference |
Citations:
Zbl 0499.62038References:
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