Polynomial Sieves as Universal Predictors

Abstract

This paper shows that polynomial sieve estimators can predict arbitrary continuous functions on closed and bounded subsets of the reals. These predictions can be arbitrarily close irrespective of whether the sieve is estimated on the full domain or a strict and non-dense subset of the domain. This result substantially generalizes the applicability of polynomial sieve estimators. The paper also provides a method to determine the accuracy of the prediction given the limits of the data used.

Keywords: prediction, polynomials, sieve estimators

JEL Classification: C45, C53