A0940
Title: Model selection based on quadratic distances
Authors: Marianthi Markatou - University at Buffalo (United States) [presenting]
Abstract: Statistical distances, divergencies, and similar quantities have a large history and play a fundamental role in statistics, machine learning, and associated scientific disciplines. The focus is on the role of quadratic distances, a special class of statistical distances, on robust model selection, and a method called quadratic information criterion (QIC) is proposed. This method is derived as a suitable estimator of the relative quadratic risk, the definition of which is based on the concept of quadratic distance between two probability distributions. The construction of QIC is discussed, and it is shown that, for specific values of the tuning parameter, QIC is equivalent to AIC and asymptotically equivalent to BIC. Using oracle inequalities in the regression case, a specific form of QIC is proposed for practical use. Simulation results and application of this criterion to real data sets indicate better performance than BIC in small data sets and equivalent to BIC performance in larger data sets in the regression context. Furthermore, the QIC clearly outperforms both the AIC and the corrected AIC.
