Sankhya: The Indian Journal of Statistics

1996, Volume 58, Series A, Pt. 1, pp. 149--159

AN OPTIMAL POWER ZONE OF NORMAL CONVERGENCE FOR SIGNED RANK STATISTICS WITH REGRESSION CONSTANTS

By

MUNSUP SEOH, Wright State University

SUMMARY.  An optimal range is shown to be $0 < x \leq o(N_1/4)$ as the power zone of normal convergence (see Petrov (1975) for the terminology) for linear signed rank statistics under the null hypothesis of symmetry. The results obtained are valid with a broad range of regression constants as well as a broad range of scores restricted by very mild conditions (scores are allowed to be generated by discontinuous score functions, but not necessarily), while most of the previous results for the problem dealing with rank statistics are obtained either with rank statistics are obtained either with severely restricted regression constants or with a narrow range of scores generated by bounded and continuously differentiable functions.

AMS (1980) subject classification.  Primary 60F10, secondary 62E20.

Key words and phrases. Linear signed rank statistics, regression constants, discontinuous score function, power zone of normal convergence, large deviation probability.

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