- Convergence of generalized Orlicz norms with decrease development fee tending to infinity(arXiv)
Writer : Giacomo Bertazzoni, Petteri Harjulehto, Peter Hästö
Summary : We research convergence of generalized Orlicz energies when the decrease growth-rate tends to infinity. We generalize outcomes by Bocea — Mihăilescu (Orlicz case) and Eleuteri — Prinari (variable exponent case) and permit weaker assumptions: we’re additionally in a position to deal with unbounded domains with irregular boundary and non-doubling energies.
2.Tight Focus Inequality for Sub-Weibull Random Variables with Generalized Bernstien Orlicz norm (arXiv)
Writer : Heejong Bong, Arun Kumar Kuchibhotla
Summary : Current growth in high-dimensional statistical inference has necessitated focus inequalities for a broader vary of random variables. We give attention to sub-Weibull random variables, which prolong sub-Gaussian or sub-exponential random variables to permit heavy-tailed distributions. This paper presents focus inequalities for impartial sub-Weibull random variables with finite Generalized Bernstein-Orlicz norms, offering generalized Bernstein’s inequalities and Rosenthal-type second bounds. The tightness of the proposed bounds is proven via decrease bounds of the focus inequalities obtained by way of the Paley-Zygmund inequality. The outcomes are utilized to a graphical mannequin inference downside, enhancing earlier pattern complexity bounds.
