Generalized fiducial inference for normal linear mixed models

By Jessi Cisewski, Jan Hannig. 2012

48 citations recorded by the source corpus.

While linear mixed modeling methods are foundational concepts introduced in any statistical education, adequate general methods for interval estimation involving models with more than a few variance components are lacking, especially in the unbalanced setting. Generalized fiducial inference provides a possible framework that accommodates this absence of methodology. Under the fabric of generalized fiducial inference along with sequential Monte Carlo methods, we present an approach for interval estimation for both balanced and unbalanced Gaussian linear mixed models. We compare the proposed method to classical and Bayesian results in the literature in a simulation study of two-fold nested models and two-factor crossed designs with an interaction term. The proposed method is found to be competitive or better when evaluated based on frequentist criteria of empirical coverage and average length of confidence intervals for small sample sizes. A MATLAB implementation of the proposed algorithm is available from the authors.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/216675e83c6e4d9fa228e8193beb09d2843335d4

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Group bound: confidence intervals for groups of variables in sparse high dimensional regression without assumptions on the design (2013, background): “For a known noise distribution, the noise vector is clearly a pivotal quantity and this is exploited in the argument above and could possibly be extended to fiducial-type inference (Cisewski and Hannig, 2012; Wang et al., 2012; Taraldsen and Lindqvist, 2013).”
Generalized Fiducial Inference: A Review and New Results (2016, methodology): “…has also been applied to derive confidence procedures in many important statistical problems, such as variance components (E, Hannig, and Iyer 2008; Cisewski and Hannig 2012), maximum mean of a multivariate normal distribution (Wandler and Hannig 2011), multiple comparisons (Wandler and Hannig…”