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Confidence Intervals on Ratios of Variance Components for the Unbalanced Two Factor Nested Model
Author(s) -
Sen Bhabesh,
Graybill Franklin A.,
Ting Naitee
Publication year - 1992
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710340302
Subject(s) - unobservable , confidence interval , mathematics , statistics , variance components , variance (accounting) , robust confidence intervals , econometrics , accounting , business
Abstract The model considered in this article is the two‐factor nested unbalanced variance component model:for p = 1, 2, …, P ; q = 1, 2, …, Q p ; and r = 1, 2, …, R pq . The random variables Y pqr are observable. The constant μ is an unknown parameter, and A p , B pq and C pqr are (unobservable) normal and independently distributed random variables with zero means and finite variances σ 2 A , σ 2 B , and σ 2 C , respectively. Approximate confidence intervals on ϱ A and ϱ B using unweighted means are derived, whereThe performance of these approximate confidence intervals are evaluated using computer simulation. The simulated results indicate that these proposed confidence intervals perform satisfactorily and can be used in applied problems.