Bayesian inference for variance components using only error contrasts

By D. Harville. 1974

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Citations in the corpus

Conditional variance penalties and domain shift robustness (2017, background): “In the equivalent constrained form, the estimator can be viewed as an instance of a restricted maximum likelihood estimator (Harville, 1974; Verbeke and Molenberghs, 2009).”
The Design and Analysis of Computer Experiments (2003, methodology): “typically no longer linear in the training data Y (R̂ = R̂(Y) and r̂0 = r̂0(Y ) are usually highly nonlinear in Y) nor need they be unbiased for Y(x0) (although see Kackar and Harville (1984)).”
Mixed model prediction and small area estimation (2006, methodology): “Jeske and Harville (1988) considered prediction intervals for a mixed effect, assuming the parametric distribution of α and y − E(y). Jiang and Zhang (2002) used a distribution-free method for constructing prediction intervals for a future observation under a non-Gaussian linear mixed model.”
An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem (2007, background): “In the classical statistics literature, it has been motivated as a way of compensating for the loss of degrees of freedom associated with estimating covariance components along with unknown weights analogous to [21], [22].”
Efficient Control of Population Structure in Model Organism Association Mapping (2008, methodology): “A derivation of Equations 6 and 7 from Equations 2 and 3 is presented in P atterson and T hompson (1971) and H arville (1974).”
Objective Bayesian Analysis of Spatially Correlated Data (2001, background): “Finally, note that Harville (1974) shows that if S D I ƒ X4X 0 X5 ƒ 1 X 0 and A is the n 4n ƒ p5 matrix satisfying AA 0 D S and A 0 A D I , then the random vector A 0 Z of n ƒ p linearly independent error contrasts has a sampling distribution proportional to (5), obviating any concerns about the…”
A General Statistical Analysis for fMRI Data (2000, unknown): “If σ(2) random is unknown then we can estimate γ and σ 2 random by restricted maximum likelihood (REML) (Harville, 1974), which gives less biased variance estimates than maximum likelihood (ML).”
Structured Additive Regression for Categorical Space–Time Data: A Mixed Model Approach (2006, unknown): “But, as Harville (1974) showed, the concept of restricted maximum likelihood is equivalent to maximizing the marginal likelihood L∗(Λ) = ∫ L(β, β,Λ)dβdβ.”
Non-negative least-squares variance component estimation with application to GPS time series (2016, methodology): “This estimator can be shown to converge locally to the results of the other existing VCE methods such as LS-VCE, MINQUE, BIQUE or REML estimates (see Koch 1986, 1987, 1999; Ou 1989).”