Sieve likelihood ratio inference on general parameter space

Abstract

In this paper, a theory on sieve likelihood ratio inference on general parameter spaces (including infinite dimensional) is studied. Under fairly general regularity conditions, the sieve log-likelihood ratio statistic is proved to be asymptotically χ 2 distributed, which can be viewed as a generalization of the well-known Wilks' theorem. As an example, a semiparametric partial linear model is investigated.