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Abstract:
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High dimensional data routinely arises in multiparameter Bayesian models, genetic experiments, image analysis and various other research areas. Statistical inference in these topics generally calls for a location parameter estimation, along with finding an appropriate credible set. Multivariate quantiles are typically used for this purpose, however all versions of such quantiles have their limitations. In many cases, high dimensionality and lack of adequate number of observations pose computational and stability problems. We develop a new principle that unifies and generalizes some existing notions of multivariate quantiles, and leads to some algorithmic advantages over existing methods. We study theoretically and in several examples the comparative performance of different multivariate quantile methods, in terms of the volume and the coverage of credible sets.
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