ABSTRACT
This chapter presents methods based on the embedding principle. It starts with the EM-Algorithm (expectation-maximization), where the observed model is embedded in the complete model. The theoretical background of EM is given, and the EM algorithm for mixture models is derived. The relation between MC and EM is demonstrated in the MCEM algorithm. Another idea of a simulation method is explored by the SIMEX method (Simulation-Extrapolation estimation), where the data are disturbed in a controlled way.
The last section of this chapter contains the variable selection methods. First, the standard F-Backwards and F-Forward procedures are presented. Wu's FSR-forward procedure explores pseudo-variables for estimating the false selecting rate, FSR. The SimSel method combines the ideas of SIMEX and of Wu's method for performing a variable selection based on controlled perturbation of the variable under consideration, in comparison with controlled perturbation of a pseudo-variable.
The underlying theoretical background of the various methods are explained. All methods are demonstrated with a series of examples and plots. Some of the most important R codes are given. The chapter ends with a list of problems useful for written exams.
