We propose kernel-type smoothed Kolmogorov-Smirnov and Cramér-von Mises tests for data on general interval, using bijective transformations. Though not as severe in the kernel density estimation, utilizing naive method directly to those particular will result boundary problem well. This happens mostly because value of distribution function estimator is still larger than 0 (or less 1) when it ev...

Robin J. DEELEY †, Joshua T. HORWOOD ‡, Raymond G. MCLENAGHAN † and Roman G. SMIRNOV § † Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada E-mail: [email protected], [email protected] ‡ Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 OWA, United Kingdom E-mail: jh423@ca...

Alexander Kurz, Tao Liu, Peter Marquard, Alexander V. Smirnov, Vladimir A. Smirnov, and Matthias Steinhauser Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany Deutsches Elektronen Synchrotron DESY, Platanenallee 6, 15738 Zeuthen, Germany Scientific Research Computing Center, Moscow State University, 119991, Moscow, Russia Skobeltsyn Inst...

We give sharp, uniform estimates for the probability that the empirical distribution function for n uniform-[0, 1] random variables stays to one side of a given line.

We study real Smirnov functions and investigate a certain ∗-closed subalgebra of the Smirnov class N+ containing them. Motivated by a result of Aleksandrov, we provide an explicit representation for the space Hp ∩ Hp. This leads to a natural analog of the Riesz projection on a certain quotient space of Lp for p ∈ (0, 1). We also study a Herglotz-like integral transform for singular measures on ...

We introduce canonical antisymmetric quasiconformal maps, which minimize the quasiconformality constant among maps sending the unit circle to a given quasicircle. As an application we prove Astala's conjecture that the Hausdorff dimension of a $k$-quasicircle is