Estimation of covariance matrices

Mathilde Bouriga and Olivier Féron have posted a paper on arXiv centred on the estimation of covariance matrices using inverse-Wishart priors. They introduce hyperpriors on the hyperparameters in the spirit of Daniels and Kass (JASA, 1999) and derive Bayes estimators as well as MCMC procedures. They then run a simulation comparison between the different priors in terms of frequentist risks, concluding in favour of the shrinkage covariance estimators that shrink all components of the empirical covariance matrix. (This paper is part of Mathilde’s thesis, which I co-advise with Jean-Michel Marin.)

More among interesting postings on arXiv, many of them published in Statistical Science:

3 Responses to “Estimation of covariance matrices”

  1. Quantitative geneticists have been estimating (genetic) covariance matrices for decades and been confronted to this problem. A recent paper that suggests shrunken estimators is here

    http://www.genetics.org/content/185/3/1097

    and references therein.

  2. Dan Simpson Says:

    I’m struggling with the model in “Variable Selection for Nonparametric Gaussian Process Priors: Models and Computational Strategies”…

    As far as I can see, they’re modelling relationships between *covariates* using a GP prior. This necessitates a ‘closeness’ in covariate space that is really hard for me to get my head around – what is the metric between wind speed and the GDP of Kenya? Even if there is a ‘closeness’, the variable selection model doesn’t make sense under ‘infill’ conditions.

    Am I missing something?

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