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August 1997 Wald consistency and the method of sieves in REML estimation
Jiming Jiang
Ann. Statist. 25(4): 1781-1803 (August 1997). DOI: 10.1214/aos/1031594742

Abstract

We prove that for all unconfounded balanced mixed models of the analysis of variance, estimates of variance components parameters that maximize the (restricted) Gaussian likelihood are consistent and asymptotically normal--and this is true whether normality is assumed or not. For a general (nonnormal) mixed model, we show estimates of the variance components parameters that maximize the (restricted) Gaussian likelihood over a sequence of approximating parameter spaces (i.e., a sieve) constitute a consistent sequence of roots of the REML equations and the sequence is also asymptotically normal. The results do not require the rank p of the design matrix of fixed effects to be bounded. An example shows that, in some unbalanced cases, estimates that maximize the Gaussian likelihood over the full parameter space can be inconsistent, given the condition that ensures consistency of the sieve estimates.

Citation

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Jiming Jiang. "Wald consistency and the method of sieves in REML estimation." Ann. Statist. 25 (4) 1781 - 1803, August 1997. https://doi.org/10.1214/aos/1031594742

Information

Published: August 1997
First available in Project Euclid: 9 September 2002

zbMATH: 0890.62020
MathSciNet: MR1463575
Digital Object Identifier: 10.1214/aos/1031594742

Subjects:
Primary: 62F12

Keywords: mixed models , restricted maximum likelihood , the method of sieves , Wald consistency

Rights: Copyright © 1997 Institute of Mathematical Statistics

Vol.25 • No. 4 • August 1997
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