24,401 research outputs found
Tests based on characterizations, and their efficiencies: a survey
A survey of goodness-of-fit and symmetry tests based on the characterization
properties of distributions is presented. This approach became popular in
recent years. In most cases the test statistics are functionals of
-empirical processes. The limiting distributions and large deviations of new
statistics under the null hypothesis are described. Their local Bahadur
efficiency for various parametric alternatives is calculated and compared with
each other as well as with diverse previously known tests. We also describe new
directions of possible research in this domain.Comment: Open access in Acta et Commentationes Universitatis Tartuensis de
Mathematic
Harper-Hofstadter problem for 2D electron gas with -linear Rashba spin-orbit coupling
The Harper-Hofstadter problem for two-dimensional electron gas with Rashba
spin-orbit coupling subject to periodic potential and perpendicular magnetic
field is studied analytically and numerically. The butterfly-like energy
spectrum, spinor wave functions as well as the spin density and average spin
polarization are calculated for actual parameters of semiconductor structure.
Our calculations show that in two-dimensional electron gas subject to periodic
potential and uniform magnetic field the effects of energy spectrum splitting
caused by large spin-orbit Rashba coupling can be observed experimentally.Comment: 8 pages, 6 figures. submitted to Europhys. Letter
New -empirical tests of symmetry based on extremal order statistics, and their efficiencies
We use a characterization of symmetry in terms of extremal order statistics
which enables to build several new nonparametric tests of symmetry. We discuss
their limiting distributions and calculate their local exact Bahadur efficiency
under location alternative which is mostly high.Comment: 17 page
- …