Adaptive Covariance Estimation with model selection

We provide in this paper a fully adaptive penalized procedure to select a covariance among a collection of models observing i.i.d replications of the process at fixed observation points. For this we generalize previous results of Bigot and al. and propose to use a data driven penalty to obtain an oracle inequality for the estimator. We prove that this method is an extension to the matricial regression model of the work by Baraud

A comparison of block and semi-parametric bootstrap methods for variance estimation in spatial statistics

Efron (1979) introduced the bootstrap method for independent data but it cannot be easily applied to spatial data because of their dependency. For spatial data that are correlated in terms of their locations in the underlying space the moving block bootstrap method is usually used to estimate the precision measures of the estimators. The precision of the moving block bootstrap estimators is related to the block size which is difficult to select. In the moving block bootstrap method also the variance estimator is underestimated. In this paper, first the semi-parametric bootstrap is used to estimate the precision measures of estimators in spatial data analysis. In the semi-parametric bootstrap method, we use the estimation of the spatial correlation structure. Then, we compare the semi-parametric bootstrap with a moving block bootstrap for variance estimation of estimators in a simulation study. Finally, we use the semi-parametric bootstrap to analyze the coal-ash data

Simulation of Auger decay dynamics in the hard X-ray regime: HCl as a showcase

Auger decay after photoexcitation or photoemission of an electron from a deep inner shell in the hard X-ray regime can be rather complex, implying a multitude of phenomena such as multiple-step cascades, post-collision interaction (PCI), and electronic state-lifetime interference. Furthermore, in a molecule nuclear motion can also be triggered. Here we discuss a comprehensive theoretical method which allows us to analyze in great detail Auger spectra measured around an inner-shell ionization threshold. HCl photoexcited or photoionized around the deep Cl 1s threshold is chosen as a showcase. Our method allows calculating Auger cross sections considering the nature of the ground, intermediate and final states (bound or dissociative), and the evolution of the relaxation process, including both electron and nuclear dynamics. In particular, we show that we can understand and reproduce a so-called experimental 2D-map, consisting of a series of resonant Auger spectra measured at different photon energies, therefore obtaining a detailed picture of all above-mentioned dynamical phenomena at once

Postcollision interaction effects in KLL Auger spectra following argon 1s photoionization

Postcollision interaction effects on the Auger decay of a deep core hole are studied both experimentally and theoretically. KL2,3L2,3 decay spectra of the Ar 1s vacancy are measured with high-energy resolution with excess photon energies ranging from 0 to 200 eV above the ionization threshold. Interaction of the Auger electron with the photoelectron and the ion field manifests itself in the Auger spectra as a distortion of the energy distribution of the Auger electron close to threshold. Moreover, recapture of the photoelectron due to energy exchange is dominating in the low-photon-energy range above threshold. The experimental results are compared with calculations based on the semiclassical approach to the postcollision interaction. The energies of the discrete levels and individual recapture cross sections are computed in the Hartree-Fock approximation. Good agreement is found between the calculated and experimental spectra, validating the model used

Two-to-one Auger decay of a double L vacancy in argon

We have observed L223−M3 Auger decay in argon where a double vacancy is filled by two valence electrons and a single electron is ejected from the atom. A well-resolved spectrum of these two-to-one electron transitions is compared to the result of the second-order perturbation theory and its decay branching ratio is determined

Double-core-hole states in CH3CN: Pre-edge structures and chemical-shift contributions

Spectra reflecting the formation of single-site double-core-hole pre-edge states involving the N 1s and C 1s core levels of acetonitrile have been recorded by means of high-resolution single-channel photoelectron spectroscopy using hard X-ray excitation. The data are interpreted with the aid of ab initio quantum chemical calculations, which take into account the direct or conjugate nature of this type of electronic states. Furthermore, the photoelectron spectra of N 1s and C 1s singly core-ionized states have been measured. From these spectra, the chemical shift between the two C 1s−1 states is estimated. Finally, by utilizing C 1s single and double core-ionization potentials, initial and final state effects for the two inequivalent carbon atoms have been investigated