Abstract
The orthonormal Legendre polynomial system is incorporated in the formulationf of signed rank statistics for asymptoticaly efficient testing and estimation procedures for the location parameter (or the intercept parameter in a linear model). A well defined stopping rule relates to an adaptive, sequential procedure for the choice of a finite set of terms and the related score function. Some refined asymptotic linearity results( in location as well as regression parameters) on signed rank staistics (with reference to the Legendre polynomial system) are established, and their role in the proposed (sequentially adaptive) procedure is thoroughly discussed.
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