The Annals of Mathematical Statistics

Mixed Model Variance Analysis with Normal Error and Possibly Non-Normal Other Random Effects: Part II: The Multivariate Case

S. N. Roy and Whitfield Cobb

Full-text: Open access

Abstract

The present paper is a continuation of another with similar title and the same overall objectives--confidence bounds on appropriate measures of the dispersion of the distribution from which random (block) effects are drawn in an experiment where fixed (treatment) effects are also under investigation. Specifically, confidence bounds are obtained on the maximum and minimum characteristic roots of the variance matrix of the block effects when the latter are assumed to come from a $p$-variate normal distribution (without the assumption made in [1], [5] that this variance matrix is proportional to that of the error). When the random block effects are not assumed to be normal, consideration is given to the approximation of an unknown multivariate distribution by means of marginal and conditional quantiles. Then for a rather restricted bivariate case, simultaneous confidence bounds are found for the two interquartile ranges. Since the ideas and notation of the first paper are presupposed by this one, much duplication is avoided by reference to appropriate sections or steps in the previous article. To facilitate such reference, the numbering is consecutive through both parts.

Article information

Source
Ann. Math. Statist., Volume 31, Number 4 (1960), 958-968.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177705669

Digital Object Identifier
doi:10.1214/aoms/1177705669

Mathematical Reviews number (MathSciNet)
MR141200

Zentralblatt MATH identifier
0249.62077

JSTOR
links.jstor.org

Citation

Roy, S. N.; Cobb, Whitfield. Mixed Model Variance Analysis with Normal Error and Possibly Non-Normal Other Random Effects: Part II: The Multivariate Case. Ann. Math. Statist. 31 (1960), no. 4, 958--968. doi:10.1214/aoms/1177705669. https://projecteuclid.org/euclid.aoms/1177705669


Export citation

See also

  • Part I: S. N. Roy, Whitfield Cobb. Mixed Model Variance Analysis with Normal Error and Possibly Non-Normal Other Random Effects: Part I: The Univariate Case. Ann. Math. Statist., Volume 31, Number 4 (1960), 939--957.