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June, 1982 The Asymptotic Effect of Substituting Estimators for Parameters in Certain Types of Statistics
Donald A. Pierce
Ann. Statist. 10(2): 475-478 (June, 1982). DOI: 10.1214/aos/1176345788

Abstract

In a variety of statistical problems, one is interested in the limiting distribution of statistics $\hat{T}_n = T_n(y_1, y_2, \cdots, y_n; \hat{\lambda}_n)$, where $\hat{\lambda}_n$ is an estimator of a parameter in the distribution of the $y_i$ and where the limiting distribution of $T_n = T_n(y_1, y_2, \cdots, y_n; \lambda)$ is relatively easy to find. For cases in which the limiting distribution of $T_n$ is normal with mean independent of $\lambda$, a useful method is given for finding the limiting distribution of $\hat{T}_n$. A simple application to testing normality in regression models is given.

Citation

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Donald A. Pierce. "The Asymptotic Effect of Substituting Estimators for Parameters in Certain Types of Statistics." Ann. Statist. 10 (2) 475 - 478, June, 1982. https://doi.org/10.1214/aos/1176345788

Information

Published: June, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0488.62012
MathSciNet: MR653522
Digital Object Identifier: 10.1214/aos/1176345788

Subjects:
Primary: 62E20
Secondary: 62F05

Rights: Copyright © 1982 Institute of Mathematical Statistics

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Vol.10 • No. 2 • June, 1982
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