A Bistochastic Nonparametric Estimator

We explore the relevance of adopting a bistochastic nonparametric estimator. This estimator has two main implications. First, the estimator reduces variability according to the robust criterion of second-order stochastic (and Lorenz) dominance. This is a universally criterion in risk and welfare economics, which expands the applicability of nonparametric estimation in economics, for instance to the measurement of economic discrimination. Second, the bistochastic estimator produces smaller errors than do positive-weights nonparametric estimators, in terms of the bias-variance trade-off. This result is verified in a general simulation exercise. This improvement is due to a significant reduction in boundary bias, which makes the estimator itself useful in empirical applications. Finally, consistency, preservation of the mean value, and multidimensional extension are some other useful properties of this estimator.