Qualitative robustness of statistical functionals under strong mixing

A new concept of (asymptotic) qualitative robustness for plug-in estimators based on identically distributed possibly dependent observations is introduced, and it is shown that Hampel's theorem for general metrics $d$ still holds. Since Hampel's theorem assumes the UGC property w.r.t. $d$, that is, convergence in probability of the empirical probability measure to the true marginal distribution w.r.t. $d$ uniformly in the class of all admissible laws on the sample path space, this property is shown for a large class of strongly mixing laws for three different metrics $d$. For real-valued observations, the UGC property is established for both the Kolomogorov $\phi$-metric and the L\'{e}vy $\psi$-metric, and for observations in a general locally compact and second countable Hausdorff space the UGC property is established for a certain metric generating the $\psi$-weak topology. The key is a new uniform weak LLN for strongly mixing random variables. The latter is of independent interest and relies on Rio's maximal inequality.Comment: Published at http://dx.doi.org/10.3150/14-BEJ608 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Hybridization and Depth-Related Effects of Surface and Impurity-Localized Modes in Finite Tight-Binding Chain

Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę

Advantages to Be Gained from the Selective Spin-Wave Resonance Critical Angles Effect

We show that the exchange constant and surface anisotropy constants of a thin ferromagnetic film can be determined by measuring the critical angles at which the successive spin-wave mode peaks vanish.Zadanie pt. Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę