The Annals of Statistics

Maximin clusters for near-replicate regression lack of fit tests

Forrest R. Miller, James W. Neill, and Brian W. Sherfey

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Abstract

To assess the adequacy of a nonreplicated linear regression model, Christensen introduced the concepts of orthogonal between- and within-cluster lack of fit with corresponding optimal tests. However, the properties of these tests depend on the choice of near-replicate clusters. In this paper, a graph theoretic framework is presented to represent candidate clusterings. A clustering is then selected according to a proposed maximin power criterion from among the clusterings consistent with a specified graph on the predictor settings. Examples are given to illustrate the methodology.

Article information

Source
Ann. Statist., Volume 26, Number 4 (1998), 1411-1433.

Dates
First available in Project Euclid: 21 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1024691249

Digital Object Identifier
doi:10.1214/aos/1024691249

Mathematical Reviews number (MathSciNet)
MR1647726

Zentralblatt MATH identifier
0932.62075

Subjects
Primary: 62J05: Linear regression
Secondary: 62F03: Hypothesis testing

Keywords
Regression lack of fit nonreplication between clusters within clusters maximin power graph theory

Citation

Miller, Forrest R.; Neill, James W.; Sherfey, Brian W. Maximin clusters for near-replicate regression lack of fit tests. Ann. Statist. 26 (1998), no. 4, 1411--1433. doi:10.1214/aos/1024691249. https://projecteuclid.org/euclid.aos/1024691249


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  • MANHATTAN, KANSAS 66506-0802 KANSAS STATE UNIVERSITY
  • MANHATTAN, KANSAS 66506-0802 E-MAIL: jwneill@stat.ksu.edu