An improved approximation to the precision of fixed effects from restricted maximum likelihood

An approximate small sample variance estimator for fixed effects from the multivariate normal linear model, together with appropriate inference tools based on a scaled F pivot, is now well established in practice and there is a growing literature on its properties in a variety of settings. Although...

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Bibliographic Details
Published in:Computational statistics & data analysis Vol. 53; no. 7; pp. 2583 - 2595
Main Authors: Kenward, Michael G., Roger, James H.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.05.2009
Elsevier
Series:Computational Statistics & Data Analysis
Subjects:
Exact sciences and technology
General topics
Linear inference, regression
Mathematics
Multivariate analysis
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Probability and statistics
Sciences and techniques of general use
Statistics
Data analysis
Approximation
Covariance analysis
Variance estimation
Bias
Taylor series
Statistical estimation
Invariance
Multivariate analysis
Statistical simulation
Fixed effect
Variance analysis
Linear model
Variance
Statistical regression
Statistical computation
Covariance
Series expansion
Small sample
Maximum likelihood
Mathematical expansion
Expansion
Biased estimation
ISSN:0167-9473, 1872-7352
Online Access:Get full text
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Summary:An approximate small sample variance estimator for fixed effects from the multivariate normal linear model, together with appropriate inference tools based on a scaled F pivot, is now well established in practice and there is a growing literature on its properties in a variety of settings. Although effective under linear covariance structures, there are examples of nonlinear structures for which it does not perform as well. The cause of this problem is shown to be a missing term in the underlying Taylor series expansion which accommodates the bias in the estimators of the parameters of the covariance structure. The form of this missing term is derived, and then used to adjust the small sample variance estimator. The behaviour of the resulting estimator is explored in terms of invariance under transformation of the covariance parameters and also using a simulation study. It is seen to perform successfully in the way predicted from its derivation.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2008.12.013