Sieve extremum estimation

Abstract

Semi-nonparametric models are more flexible and robust than parametric models, but are more complex due to the presence of infinite dimensional unknown parameters. This article describes the method of sieve extremum estimation of semi-nonparametric models, which is a general method of optimizing an empirical criterion function over a sequence of approximating parameter spaces (that is, sieves). Widely used sieve spaces and criterion functions are presented as examples, including the sieve M-estimation, series estimation, and sieve minimum distance estimation as special cases. Existing results are cited on asymptotic properties and applications of the method.