Approximation of information divergences for statistical learning with applications

Year, pages: 2018, 1149 - 1172

In 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.

Stehlík, M., Somorčík, J., Střelec, L., Antoch, J. 2018. Approximation of information divergences for statistical learning with applications. In Mathematica Slovaca, vol. 68, no.5, pp. 1149-1172. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0177

Stehlík, M., Somorčík, J., Střelec, L., Antoch, J. (2018). Approximation of information divergences for statistical learning with applications. Mathematica Slovaca, 68(5), 1149-1172. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0177