MLE for User-Defined Likelihood Functions

Introduction

MLE for User-Defined Likelihood Functions

There are three SAS procedures that enable you to do maximum likelihood estimation of parameters in an arbitrary model with a likelihood function that you define: PROC MODEL, PROC NLP, and PROC IML.

Maximum likelihood can often be cast as an equivalent least squares problem through the use of appropriate transformations. The MODEL procedure in SAS/ETS software enables you to minimize a sum of squares function. If you can write a sum of squares function that is minimized when the likelihood function is maximized, then you can use the MODEL procedure in SAS/ETS software.

The NLP procedure in SAS/OR software is a general nonlinear programming procedure that can maximize a general function subject to linear equality or inequality constraints. You can use PROC NLP to maximize a user-defined nonlinear likelihood function.

You can use the IML procedure in SAS/IML software for maximum likelihood problems. The optimization routines used by PROC NLP are available through IML subroutines. You can write the likelihood function in the SAS/IML matrix language and call the constrained and unconstrained nonlinear programming subroutines to maximize the likelihood function with respect to the parameter vector.

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