Likelihood inference for small variance components
Likelihood inference for small variance components
In this paper, we develop likelihood-based methods for making inferences about the components of variance in a general normal mixed linear model. In particular, we use local asymptotic approximations to construct confidence intervals for the components of variance when the components are close to the boundary of the parameter space. In the process, we explore the question of how to profile the restricted likelihood (REML), show that general REML estimates have a lower probability of being on the boundary than maximum likelihood estimates, and show that the likelihood-ratio test based on the local asymptotic approximation has higher power against local alternatives than the likelihood-ratio test based on the usual chi-squared approximation. We explore the finite sample properties of the proposed intervals by means of a small simulation study.
517-532
Stern, S.E.
2f22bb7d-4b0d-4815-98d9-e1e07285fd8b
Welsh, A.H.
27640871-afff-4d45-a191-8a72abee4c1a
2000
Stern, S.E.
2f22bb7d-4b0d-4815-98d9-e1e07285fd8b
Welsh, A.H.
27640871-afff-4d45-a191-8a72abee4c1a
Stern, S.E. and Welsh, A.H.
(2000)
Likelihood inference for small variance components.
Canadian Journal of Statistics, 28, .
Abstract
In this paper, we develop likelihood-based methods for making inferences about the components of variance in a general normal mixed linear model. In particular, we use local asymptotic approximations to construct confidence intervals for the components of variance when the components are close to the boundary of the parameter space. In the process, we explore the question of how to profile the restricted likelihood (REML), show that general REML estimates have a lower probability of being on the boundary than maximum likelihood estimates, and show that the likelihood-ratio test based on the local asymptotic approximation has higher power against local alternatives than the likelihood-ratio test based on the usual chi-squared approximation. We explore the finite sample properties of the proposed intervals by means of a small simulation study.
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STAT2000-01.pdf
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Published date: 2000
Organisations:
Statistics
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Local EPrints ID: 29929
URI: http://eprints.soton.ac.uk/id/eprint/29929
PURE UUID: 6a632ec2-3977-455c-aabd-2b539b148ff6
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Date deposited: 16 Mar 2007
Last modified: 15 Mar 2024 07:36
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Author:
S.E. Stern
Author:
A.H. Welsh
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