Krause, Rudiger

Genetic Algorithms as Tool for Statistical Analysis of High-Dimensional Data Structures

In regression the objective is to determine an appropriate functionwhich reflects reality as accurate as possible but also eliminatesirregularities from data noise and is therefore easy to interpret.A popular and flexible approach for estimating the true underlyingfunction is the additive model. One possible approach for fittingadditive models is the expansion in B-splines which allows directcalculation of the estimators. If the number of B-splines is toolarge the estimated functions become wiggly and tend to be veryclose to the observed data. To avoid this problem of overfittingwe use a penalization approach characterized by smoothing parameters.In this thesis we propose the use of genetic algorithmsfor smoothing parameter optimization. Genetic algorithms are rarelyapplied in the field of statistics and refer to the principle thatbetter adapted individuals win against their competitorsunder equal conditions. Apart from smoothing parameteroptimization the user often faces datasets containing large numbersof relevant and irrelevant explanatory variables. Appropriate variableselection approaches allow to reduce the number of variables tosubsets of relevant variables. We propose to consider the problems ofvariable selection and choice of smoothing parameters simultaneouslyby using genetic algorithms. Our approach bases on an appropriatecombination of the genetic algorithms for smoothing parameteroptimization and variable selection.