Semi-nonparametric Maximum Likelihood Estimation.

Often maximum likelihood is the method of choice for fitting an econometric model to data but cannot be used because the correct specific ation of (multivariate) density that defines the likelihood is unknown. In this situation, simply put the density equal to a Hermite series and apply standard finite dimensional maximum likelihood methods. Model parameters and nearly all aspects of the unknown density itself will be estimated consistently provided that the length of the series increases with sample size. The rule for increasing series length can be data dependent. The method is applied to nonlinear regression with sample selection. Copyright 1987 by The Econometric Society.