Translator Disclaimer
March, 1987 On the Effect of Substituting Parameter Estimators in Limiting $\chi^2 U$ and $V$ Statistics
Tertius de Wet, Ronald H. Randles
Ann. Statist. 15(1): 398-412 (March, 1987). DOI: 10.1214/aos/1176350274

Abstract

Consider statistics $T_n(\lambda)$ that take the form of limiting chi-square (degenerate) $U$ or $V$ statistics. Here the phrase "limiting chi-square" means they have the same asymptotic distribution as a weighted sum of (possibly infinitely many) independent $\chi^2_1$ random variables. This paper examines the limiting distribution of $T_n(\hat{\lambda})$ and compares it to that of $T_n(\lambda)$, where $\hat{\lambda}$ denotes a consistent estimator of $\lambda$ based on the same data. Whether or not $T_n(\hat{\lambda})$ and $T_n(\lambda)$ have the same limiting distribution is primarily a question of whether or not a certain mean function has a zero derivative. Some statistics that are appropriate for testing hypotheses are used to illustrate the theory.

Citation

Download Citation

Tertius de Wet. Ronald H. Randles. "On the Effect of Substituting Parameter Estimators in Limiting $\chi^2 U$ and $V$ Statistics." Ann. Statist. 15 (1) 398 - 412, March, 1987. https://doi.org/10.1214/aos/1176350274

Information

Published: March, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0617.62017
MathSciNet: MR885745
Digital Object Identifier: 10.1214/aos/1176350274

Subjects:
Primary: 62E20
Secondary: 62G10

Rights: Copyright © 1987 Institute of Mathematical Statistics

JOURNAL ARTICLE
15 PAGES


SHARE
Vol.15 • No. 1 • March, 1987
Back to Top