A probabilistic nonparametric estimator

Resumen

This paper explores the adoption of a probabilistic nonparametric estimator in economics. First, it satisfies the probabilistic coherence principle, which ensures that the estimated variable can be generated by probabilistic assignment modeling from the observed variable. Second, it is proved to reduce variability in terms of noise, majorization and Lorenz dominance principles if, and only if, the estimator is probabilistic. The latter principles are universal criteria in risk and welfare economics, which expands the applicability of the estimator; for instance, to the measurement of economic discrimination. It also guarantees the symmetrical treatment of observations, a process that can produce smaller errors than positive-weight nonparametric estimators in terms of the biasvariance trade-off. This is verified by a general simulation exercise, with improvement due to the significant reduction in boundary bias. Finally, the estimator displays some other useful properties including consistency, preservation of the mean value, and multidimensional extension.