Open Access
Translator Disclaimer
November, 1977 Tied-Down Wiener Process Approximations for Aligned Rank Order Processes and Some Applications
Pranab Kumar Sen
Ann. Statist. 5(6): 1107-1123 (November, 1977). DOI: 10.1214/aos/1176343999

Abstract

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.

Citation

Download Citation

Pranab Kumar Sen. "Tied-Down Wiener Process Approximations for Aligned Rank Order Processes and Some Applications." Ann. Statist. 5 (6) 1107 - 1123, November, 1977. https://doi.org/10.1214/aos/1176343999

Information

Published: November, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0371.62076
MathSciNet: MR451524
Digital Object Identifier: 10.1214/aos/1176343999

Subjects:
Primary: 60B10
Secondary: 62G99

Keywords: $D\lbrack 0, 1\rbrack$ space , Aligned rank order statistics , contiguity , 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

Rights: Copyright © 1977 Institute of Mathematical Statistics

JOURNAL ARTICLE
17 PAGES


SHARE
Vol.5 • No. 6 • November, 1977
Back to Top