The Annals of Statistics

Optimum Tests in Unbalanced Two-Way Models without Interaction

Thomas Mathew and Bimal Kumar Sinha

Full-text: Open access

Abstract

It is an open problem in the literature to derive optimum tests for the equality of treatment effects in an unbalanced two-way classification model. For such models without interaction, optimum tests are derived in the following cases: (i) the locally best invariant unbiased test for the random effects model corresponding to an equiblock and equireplicate design, (ii) the locally best invariant unbiased test for the mixed effects model with mixed treatment effects corresponding to a balanced incomplete block design and (iii) the uniformly most powerful invariant test or the locally best invariant test for the mixed effects model with random treatment effects. Robustness of the optimum invariant tests against suitable deviations from normality is also indicated.

Article information

Source
Ann. Statist., Volume 16, Number 4 (1988), 1727-1740.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176351065

Digital Object Identifier
doi:10.1214/aos/1176351065

Mathematical Reviews number (MathSciNet)
MR964950

Zentralblatt MATH identifier
0653.62018

JSTOR
links.jstor.org

Subjects
Primary: 62F03: Hypothesis testing
Secondary: 62F04 62K10: Block designs

Keywords
Locally best invariant test locally best invariant unbiased test uniformly most powerful invariant test balanced incomplete block design variance balanced design

Citation

Mathew, Thomas; Sinha, Bimal Kumar. Optimum Tests in Unbalanced Two-Way Models without Interaction. Ann. Statist. 16 (1988), no. 4, 1727--1740. doi:10.1214/aos/1176351065. https://projecteuclid.org/euclid.aos/1176351065


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