Robust Procedures for Estimating and Testing in the Framework of Divergence Measures.

The Bayes error rate is the expected risk for the Bayes classifier, which assigns a given feature vector HT <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi mathvariant="bold-italic">x</mi></semantics></math> ht to the class with the highest posterior probability. The so obtained rho function is proportional to one minus a suitably scaled normal density raised to the power HT <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi> </mi></semantics></math> ht . Hence, the large deviation principle in the weak topology of HT <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>l</mi><mn>1</mn></msub></semantics></math> ht can be derived (more easily) using a standard Gartner-Ellis argument and, utilizing this, one can, in principle, repeat all of the arguments above to derive results that are analogous to Theorems 2.2 and 2.3. [Extracted from the article]