Semi-nonparametric maximum likelihood estimation. (English) Zbl 0631.62110

Gallant, A. Ronald; Nychka, Douglas W.

Econometrica 55, 363-390 (1987).

The density of Hermite forms: \[ h(u)=P^ 2_ k(u-\tau)\Phi^ 2(u| \tau,diag(\gamma)) \] where \(P_ k\) is a polynomial of degree K and \(\Phi\) is the density function of the multivariate normal distribution is shown to be capable of approximating any density arbitrarily closely subject to minimal qualifications relating to compactness, denseness, uniform convergence and identification defined over the parameter space.

Reviewer: L.Podkaminer

MSC:

62P20	Applications of statistics to economics
62G05	Nonparametric estimation
62F10	Point estimation

Keywords:

semi-nonparametric maximum likelihood estimation; Hermite series; estimation of Stoker functionals; nonlinear regression; nonparametric; semi-parametric; sample selection; fitting econometric models; Hermite forms; multivariate normal distribution; compactness; denseness; uniform convergence; identification