Nonlinear Statistical Estimation with Numerical Maximum Likelihood

The topics of maximum likelihood estimation and nonlinear programming are developed thoroughly with emphasis on the numerical details of obtaining estimates from highly nonlinear models. Parametric estimation is discussed with the three parameter Weibull family of densities serving as an example. A general nonlinear programming method is discussed for both first and second order representations of the maximum likelihood estimaton, as well as a hybrid of both approaches. A new class of constrained parametric estimators is introduced with numerical methods for their determination. Structural estimation with maximum likelihood is examined, and a Bernoulli regression technique is presented.