Linear rank statistics, finite sampling, permutation tests and Winsorizing. (English) Zbl 0862.62017

Summary: Asymptotic normality and a representation of all possible subsequential limiting distributions of a simple linear rank statistic are obtained. This is then applied to finite sampling and permutation tests for slope coefficients. The effects of Winsorizing in these situations are considered carefully. Of particular interest regarding slope coefficients is that either using normal score regression constants or Winsorizing slowly increasing numbers of the population values will guarantee asymptotic normality.


62E20 Asymptotic distribution theory in statistics
60F05 Central limit and other weak theorems
62G10 Nonparametric hypothesis testing
Full Text: DOI


[1] BREIMAN, L. 1968. Probability. Addison-Wesley, Reading, MA. Z. · Zbl 0174.48801
[2] CSORGO, S., HAEUSSLER, E. and MASON, D. 1988. A probabilistic approach to the asy mptotic \" distribution of sums of independent, identically distributed random variables. Adv. in Appl. Math. 9 259 333. Z. · Zbl 0657.60029 · doi:10.1016/0196-8858(88)90016-4
[3] CSORGO, S. and MASON, D. 1989. Bootstrapping empirical functions. Ann. Statist. 17 1447 1471. \" Z. · Zbl 0701.62057
[4] DEHEUVELS, P., MASON, D. and SHORACK, G. 1993. Some results on the influence of extremes on the bootstrap. Ann. Inst. H. Poincare Probab. Statist. 29 83 103. \' · Zbl 0774.62042
[5] HAJEK, J. and SIDAK, Z. 1967. Theory of Rank Tests. Academic Press, New York. \' Ź. · Zbl 0161.38102
[6] MASON, D. and SHORACK, G. 1992. Necessary and sufficient conditions for asy mptotic normality of L-statistics. Ann. Probab. 20 1779 1804. Z. · Zbl 0765.62024 · doi:10.1214/aop/1176989529
[7] PARDZHANADZE, A. and KHMALADZE, E. 1986. On the asy mptotic theory of statistics of sequential ranks. Theory Probab. Appl. 31 669 682. \" Z. · Zbl 0657.62051 · doi:10.1137/1131089
[8] ROSSBERG, H. 1967. Uber das asy mptotische Verhalten der Randund Zentralglieder einer Z. Variationsreihe II. Publ. Math. Debrecen 14 83 90. Z. · Zbl 0183.21501
[9] SHORACK, G. 1991a. Embedding the finite sampling process at a rate. Ann. Probab. 19 826 842. Z. · Zbl 0731.60026 · doi:10.1214/aop/1176990453
[10] SHORACK, G. 1991b. Limit results for linear combinations. In Sums, Trimmed Sums and Z. Extremes M. Hahn, D. Mason and D. Weiner, eds. 377 392. Birkhauser, Boston. \" Z. · Zbl 0724.60020
[11] SHORACK, G. and WELLNER, J. 1986. Empirical Processes with Applications to Statistics. Wiley, New York. Z. · Zbl 1170.62365
[12] ZOLATEREV, V. 1967. A generalization of the Lindeberg Feller theorem. Theory Probab. Appl. 12 608 618. · Zbl 0234.60031
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.