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We consider the problem of estimating the support of a measure from a finite,independent, sample. The estimators which are considered are constructed basedon the empirical Christoffel function. Such estimators have been proposed forthe problem of set estimation with heuristic justifications. We carry out adetailed finite sample analysis, that allows us to select the threshold anddegree parameters as a function of the sample size. We provide a convergencerate analysis of the resulting support estimation procedure. Our analysisestablishes that we may obtain finite sample bounds which are comparable toexisting rates for different set estimation procedures. Our results rely onconcentration inequalities for the empirical Christoffel function and onestimates of the supremum of the Christoffel-Darboux kernel on sets with smoothboundaries, that can be considered of independent interest.

Rate of convergence for geometric inference based on the empirical Christoffel function