  We consider the problem of estimating the support of a measure from a finite,
independent, sample. The estimators which are considered are constructed based
on the empirical Christoffel function. Such estimators have been proposed for
the problem of set estimation with heuristic justifications. We carry out a
detailed finite sample analysis, that allows us to select the threshold and
degree parameters as a function of the sample size. We provide a convergence
rate analysis of the resulting support estimation procedure. Our analysis
establishes that we may obtain finite sample bounds which are comparable to
existing rates for different set estimation procedures. Our results rely on
concentration inequalities for the empirical Christoffel function and on
estimates of the supremum of the Christoffel-Darboux kernel on sets with smooth
boundaries, that can be considered of independent interest.
