The Annals of Statistics

Wald consistency and the method of sieves in REML estimation

Jiming Jiang

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 25, Number 4 (1997), 1781-1803.

Dates
First available in Project Euclid: 9 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1031594742

Digital Object Identifier
doi:10.1214/aos/1031594742

Mathematical Reviews number (MathSciNet)
MR1463575

Zentralblatt MATH identifier
0890.62020

Subjects
Primary: 62F12: Asymptotic properties of estimators

Keywords
Mixed models restricted maximum likelihood Wald consistency the method of sieves

Citation

Jiang, Jiming. Wald consistency and the method of sieves in REML estimation. Ann. Statist. 25 (1997), no. 4, 1781--1803. doi:10.1214/aos/1031594742. https://projecteuclid.org/euclid.aos/1031594742


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