For independent random variables distributed symmetrically around an unknown location parameter, aligned rank order statistics are constructed by using an estimator of the location parameter based on suitable rank statistics. The sequence of these aligned rank order statistics is then incorporated in the construction of suitable stochastic processes which converge weakly to some Gaussian functions, and, in particular, to tied-down Wiener processes in the most typical cases. The results are extended for contiguous alternatives and then applied in two specific problems in nonparametric inference. First, the problem of testing for shift at an unknown time point is treated, and then, some sequential type asymptotic nonparametric tests for symmetry around an unknown origin are considered.
Publié le : 1977-11-14
Classification:
Aligned rank order statistics,
contiguity,
$D\lbrack 0, 1\rbrack$ space,
linearity of rank statistics,
tests for shift at an unknown point of time,
tests for symmetry around an unknown origin,
tied-down Wiener processes,
weak convergence,
60B10,
62G99
@article{1176343999,
author = {Sen, Pranab Kumar},
title = {Tied-Down Wiener Process Approximations for Aligned Rank Order Processes and Some Applications},
journal = {Ann. Statist.},
volume = {5},
number = {1},
year = {1977},
pages = { 1107-1123},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343999}
}
Sen, Pranab Kumar. Tied-Down Wiener Process Approximations for Aligned Rank Order Processes and Some Applications. Ann. Statist., Tome 5 (1977) no. 1, pp. 1107-1123. http://gdmltest.u-ga.fr/item/1176343999/