Penalized Likelihood for General Semi-Parametric Regression Models

Summary This paper examines penalized likelihood estimation in the context of general regression problems, characterized as probability models with composite likelihood functions. The emphasis is on the common situation where a parametric model is considered satisfactory but for inhomogeneity with respect to a few extra variables. A finite-dimensional formulation is adopted, using a suitable set of basis functions. Appropriate definitions of deviance, degrees of freedom, and residual are provided, and the method of cross-validation for choice of the tuning constant is discussed. Quadratic approximations are derived for all the required statistics.