Non- and Semiparametric Alternatives to Generalized Linear Models

Additive and Generalized Additive Models (GAM) are discussed as completely nonparametric alternatives to Generalized Linear Models (GLM). Single Index Models (SIM) are reviewed as a means of nonparametrically specifying the link function in GLMs. Semiparametric models with a single as well as a multiple nonparametric component are considered in some detail. The penalized least squares technique is compared to Speckman's approach to partial linear models with one unparameterized explanatory variable. Further Generalized Partial Linear Models (GPLM) are briefly mentioned. For a multiple nonparametric component a thin plate spline approach and for a dependent vector variable a vector spline approach is discussed.