DEVELOPMENT OF ROBUST STATISTICAL MODELS FOR HIGH-DIMENSIONAL DATA ANALYSIS

ABSTRACT The analysis of high dimensional genomic data, p>n, raises some challenging statistical problems. It is because of design matrix singularity and high-leverage point contamination. A new Adaptive Huber Elastic Net or the AHEN, framework was designed and tested in the case of estimating parameters and selecting variables in ultra-high-dimensional contexts. The model has been tested on all of the CuMiDa Leukemia microarray data with n = 64, p = 22,283. This is done under clean baseline conditions and contaminated conditions of 10% and 20% contamination. When severe contamination of 20% occurs, the proposed estimator has a lower baseline error of 0.5307 for CV. This is predictive when severely contaminated, while classical Ridge regression completely fails (1.6013). In addition, this modeling compressed 22,283 features down to a small number of 11.2 prognostic biomarkers. Combining bounded-influence loss and adaptive shrinkage in a unified framework is an effective approach. This basically helps with high-dimensional biomedical inference and is achieved by the proposed method. Keywords: High-Dimensional Data; Adaptive Huber Elastic Net; Robust Estimation; Variable Selection; Leukemia Microarray.