TY - JOUR AU - Antoch, Jaromír AB - AbstractIn this paper we give a partial response to one of the most important statistical questions, namely, what optimal statistical decisions are and how they are related to (statistical) information theory. We exemplify the necessity of understanding the structure of information divergences and their approximations, which may in particular be understood through deconvolution. Deconvolution of information divergences is illustrated in the exponential family of distributions, leading to the optimal tests in the Bahadur sense. We provide a new approximation of I-divergences using the Fourier transformation, saddle point approximation, and uniform convergence of the Euler polygons. Uniform approximation of deconvoluted parts of I-divergences is also discussed. Our approach is illustrated on a real data example. TI - Approximation of Information Divergences for Statistical Learning with Applications JF - Mathematica Slovaca DO - 10.1515/ms-2017-0177 DA - 2018-10-25 UR - https://www.deepdyve.com/lp/de-gruyter/approximation-of-information-divergences-for-statistical-learning-with-sVQtyGPBGk SP - 1149 EP - 1172 VL - 68 IS - 5 DP - DeepDyve ER -