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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


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.


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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.


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

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

Primary: 62E20
Secondary: 62G10

Rights: Copyright © 1987 Institute of Mathematical Statistics


Vol.15 • No. 1 • March, 1987
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