Speaker
Description
We enrich the theory of φ-divergences and statistical distances. Specifically, we explore the property of robustness of our measures used, e.g., in defectoscopy classification tasks for constructing new spectral signal attributes or in newly designed classification tree algorithm. Since almost all datasets are surely contaminated by a certain portion of some kind of noise (electronics, experimental environment, non-homogenous material, other conditions), the resistance of algorithmic decisions against possible errors or outliers is crucial. We consider the general problem of discrimination of the true statistical model or of the true data source identification under the frame of minimum distance estimators (MDE). They are increasingly being used when the classical maximum likelihood theory breaks down and because they have better robustness properties. Specifically, the power-type I$_\alpha$ and blended Le Cam φ-divergences LC$_\beta$ under six data source distributions (Uniform, Normal, Logistic, Laplace, Cauchy, 3-parametric Weibull) will be applied for sample sizes n = 10, 20, 50, 120, 250. The simulation experiment deals with the discrimination/classification capability within a semi-parametric model treated under different types of data source distributions. This simulation is based on the previously developed software package IF-M for the evaluation of different types of AMD estimators adapted for our purposes on robustness in correspondence with proven theorems.