Open Access
Translator Disclaimer
December, 1986 Asymptotic Normality of the Anova Estimates of Components of Variance in the Nonnormal, Unbalanced Hierarchal Mixed Model
Peter H. Westfall
Ann. Statist. 14(4): 1572-1582 (December, 1986). DOI: 10.1214/aos/1176350177

Abstract

Despite their lack of optimality in unbalanced normally distributed models, the ANOVA estimates of components of variance are convenient and widely used. The hierarchal (nested) design is well suited to this estimation scheme. In this paper the nonnormal, unbalanced hierarchal design is considered and mild conditions for a sequence of such designs are specified so that the vector of normalized ANOVA estimates converges to a multivariate normal distribution. The nested structure permits an expression of the estimates in terms of a sum of independent quadratic forms in mean zero random variables plus smaller order remainder, and a theorem of Whittle (1960) establishes the Liapounov criterion. Distinguishing features of this paper are the limit theory of nonnormal unbalanced models and the allowance that some variances other than the error variance may be null.

Citation

Download Citation

Peter H. Westfall. "Asymptotic Normality of the Anova Estimates of Components of Variance in the Nonnormal, Unbalanced Hierarchal Mixed Model." Ann. Statist. 14 (4) 1572 - 1582, December, 1986. https://doi.org/10.1214/aos/1176350177

Information

Published: December, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0616.62025
MathSciNet: MR868319
Digital Object Identifier: 10.1214/aos/1176350177

Subjects:
Primary: 62E20
Secondary: 62J10

Keywords: ANOVA estimates , asymptotic normality , hierarchal mixed model , variance components

Rights: Copyright © 1986 Institute of Mathematical Statistics

JOURNAL ARTICLE
11 PAGES


SHARE
Vol.14 • No. 4 • December, 1986
Back to Top