Some properties of a nonparametric estimator of the size of an open population

It has been demonstrated in the literature that local polynomial models may be used to estimate the size of an open population using capture-recapture data. However, very little is known about their properties. Here we develop a setting in which the properties of nonparametric estimators of the size of an open population using capture-recapture data can be examined and establish conditions under which expressions for the bias and variance may be determined.