Gauss-Hermite quadrature: numerical or statistical method?

Gauss-Hermite Quadrature (GHQ) is often used for numerical approximation of integrals with Gaussian kernels. In generalized linear mixed models random effects are assumed to have Gaussian distributions, but often the marginal likelihood, In addition to Monte Carlo methods, first or second order Taylor expansion, Laplace approximation or GHQ are feasible tools for numerical evaluation of the integrals. In this paper we review the key ideas of GHQ. Nonparametric Maximum Likelihood (NPML) estimation is shown to be a flexible version of GHQ. A binary nested random effects model is fitted to a real data set using GHQ.

Keywords:

Function Interpolation , Generalized Linear Mixed Model , Hermite Polynomial , Distribution , Nonparametric Maximum Likelihood.