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Effect of Non-Normality on Inferences about Variance Components

George C. Tiao and M. M. Ali
Technometrics
Vol. 13, No. 3 (Aug., 1971), pp. 635-650
DOI: 10.2307/1267174
Stable URL: http://www.jstor.org/stable/1267174
Page Count: 16
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Effect of Non-Normality on Inferences about Variance Components
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Abstract

Bayesian methods are utilized to analyse the one-way random effect model yij=μ +ai+eij in which eij are assumed normal, N(0,σ e 2), and ai are assumed to have a mixture of two normals, .95N(-.05φ (k-1)σ,σ 2)+.05N(.95φ (k-1)σ ,k2φ 2). It is shown by a moderately sized sample that inferences regarding σ e 2= var (eij) are insensitive but those of σ a 2= var (ai) are very sensitive to changes of the two non-normality parameters (k, φ). The data are also used to illustrate what inferences can be made about (k, φ). Further, for σ = 0 it is found in general that extreme observations have less importance in comparison to others in the posterior expectation of σ a 2. Finally, the ways of assessing the contributions from ai and eij to the variation of yij are considered.

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