Model selection in nonlinear regression analysis

The application of information criteria in model selection has been recognized as an important technical area. In the past decades, extensive research has been conducted to apply the criteria in linear analysis. This dissertation extends the research work into the nonlinear field, more specifically, into the nonlinear regression analysis. This dissertation concentrates on the application of the informational complexity (ICOMP) criterion due to Bozdogan (1988, 1990, 1993, 1994). For comparative purposes, the performance of ICOMP is investigated with a more classical information criterion, namely the celebrated Akaike's (1973) information criterion (AIC). In Chapter 2, parameter redundancy is defined and classified into two forms. It is shown in a theorem that ICOMP criterion works in both forms of the parameter redundancies. The impact of parameter transformation is studied in Chapter 3, where ICOMP is used in selecting a model with better geometric properties. The necessity to introduce Box-Cox transformation in the regression analysis and to choose the appropriate linearization strategy is investigated in Chapter 4. The regression model with error correlation structure is studied in Chapter 5. The results in univariate analysis are extended to the multivariate regression analysis in Chapter 6 through Chapter 8. In Chapter 7, the regression analysis of the compositional data is pre-sented, where the effect of different transformations and permutations are studied which induces models with different qualities. Chapter 8 is devoted to detect outlier and influential cases in multivariate analysis. So far, there is no well established result on this topic in the literature, and the relationship of ICOMP with a well established result in the univariate linear case is studied. It is expected that the development of the informational model selection criteria in nonlinear analysis will attract a lot of research interests by others. Conclusions are presented and future research topics in the area of nonlinear regression modeling are discussed in Chapter 9.