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Investigation of Parameter Uncertainty in Clustering Using a Gaussian Mixture Model Via Jackknife, Bootstrap and Weighted Likelihood Bootstrap.

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Adrian O'Hagan, Thomas Brendan Murphy, Luca Scrucca, Isobel Claire Gormley

Mixture models are a popular tool in model-based clustering. Such a model isoften fitted by a procedure that maximizes the likelihood, such as the EMalgorithm. At convergence, the maximum likelihood parameter estimates aretypically reported, but in most cases little emphasis is placed on thevariability associated with these estimates. In part this may be due to thefact that standard errors are not directly calculated in the model-fittingalgorithm, either because they are not required to fit the model, or becausethey are difficult to compute. The examination of standard errors inmodel-based clustering is therefore typically neglected. The widely used Rpackage mclust has recently introduced bootstrap and weighted likelihoodbootstrap methods to facilitate standard error estimation. This paper providesan empirical comparison of these methods (along with the jackknife method) forproducing standard errors and confidence intervals for mixture parameters.These methods are illustrated and contrasted in both a simulation study and inthe traditional Old Faithful data set and Thyroid data set.

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