Restricted Estimation of Generalized Linear Models

SUMMARY Maximum likelihood estimation of the generalized linear model under linear restrictions on the parameters is considered. Using a penalty function approach an iterative procedure for obtaining the estimates is proposed. The likelihood ratio test, the Wald test and the Lagrange multiplier test are considered as alternatives for testing a hypothesis about linear restrictions on the parameters. An application of the estimator and the tests is illustrated in a numerical example. The approach extends to a definition of a ridge estimator for generalized linear models and to a definition of piecewise regressions, including cubic spline functions and a nonparametric smoother.