Statistical classification in high-dimensional scenarios with a focus on microarray data sets

High-dimensional data analysis characterises many contemporary problems in statistics and arise in many application areas. This thesis focuses on very high-dimensional problems in which the input predictor variables are gene expression measurements in microarray studies. Accurate analysis of microarray data sets can provide new insight into cancer diagnosis using gene expression profiles and can result in breakthroughs in medical research. K-nearest neighbours (KNN), fastKNN, linear discriminant analysis (and variants thereof), nearest shrunken centroids (NSC) and support vector machines (SVMs) are investigated in this thesis as binary (and multi-class) classification procedures on microarray data sets. The important problem of eliminating redundant input variables before implementing classification procedures in high-dimensional data sets is addressed in this thesis. Several variable selection and dimension reduction procedures suitable for microarray data sets are discussed, with the focus on implementing sure independence techniques, NSC and fastKNN feature engineering in the empirical study. Principal component analysis and supervised principal component analysis are implemented as the two main dimension reduction techniques in this thesis. The performance of the classification procedures is evaluated on three real and three synthetic high-dimensional microarray data sets. The comparison of the different classification methods in the empirical study led to the conclusion that SVMs prove to be the most accurate procedure on the binary data sets considered, whilst NSC is the most accurate procedure on the multi-class data set.National Research Foundatio