Robustness properties of estimators in generalized Pareto Models

We study global and local robustness properties of several estimators for shape and scale in a generalized Pareto model. The estimators considered in this paper cover maximum likelihood estimators, skipped maximum likelihood estimators, moment-based estimators, Cramér-von-Mises Minimum Distance estimators, and, as a special case of quantile-based estimators, Pickands Estimator as well as variants of the latter tuned for higher finite sample breakdown point (FSBP), and lower variance. We further consider an estimator matching population median and median of absolute deviations to the empirical ones (MedMad); again, in order to improve its FSBP, we propose a variant using a suitable asymmetric Mad as constituent, and which may be tuned to achieve an expected FSBP of 34%. These estimators are compared to one-step estimators distinguished as optimal in the shrinking neighborhood setting, i.e., the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimator minimizing the maximal (asymptotic) MSE. For each of these estimators, we determine the FSBP, the influence function, as well as statistical accuracy measured by asymptotic bias, variance, and mean squared error—all evaluated uniformly on shrinking convex contamination neighborhoods. Finally, we check these asymptotic theoretical findings against finite sample behavior by an extensive simulation study

Information Geometry

This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience

The Chiral Phase Transition in QCD: Critical Phenomena and Long Wavelength Pion Oscillations

In QCD with two massless quarks, the chiral phase transition is plausibly in the same universality class as the classical O(4) magnet. To test this hypothesis, critical exponents characterizing the behaviour of universal quantities near the 2nd order critical point can be calculated and compared to results from lattice simulations. Present simulations already allow many qualitative tests; quantitative tests await future simulations with longer correlation lengths. In a heavy ion collision, a long correlation length would lead to large fluctuations in the number ratio of neutral to charged pions. Unfortunately, no equilibrium correlation length gets long enough for this to occur. Modelling the dynamics of the chiral order parameter in a far from equilibrium transition by quenching in the linear sigma model suggests that long wavelength modes of the pion field can be amplified. This could have dramatic phenomenological consequences. Theoretical advances include attempts to relax the quench approximation and to include expansion and quantum effects. Long wavelength pion oscillations arise in a number of theoretical treatments; however, all involve idealizations and are at best qualitative guides. It is up to experimentalists to determine whether such phenomena occur; detection in a heavy ion collision would imply an out of equilibrium chiral transition.Comment: References added. Review article to appear in Quark Gluon Plasma 2, edited by R. Hwa, World Scientific, 1995. latex; 12 of 14 figs include

CEAS/AIAA/ICASE/NASA Langley International Forum on Aeroelasticity and Structural Dynamics 1999

These proceedings represent a collection of the latest advances in aeroelasticity and structural dynamics from the world community. Research in the areas of unsteady aerodynamics and aeroelasticity, structural modeling and optimization, active control and adaptive structures, landing dynamics, certification and qualification, and validation testing are highlighted in the collection of papers. The wide range of results will lead to advances in the prediction and control of the structural response of aircraft and spacecraft

Hotspot detection and a nonstationary process variance function estimation

A two-stage spatial sampling design for detecting contaminated areas is proposed for effective decontamination planning. A two-stage design has a higher or equal hotspot detection probability than a one-stage design under fixed budget constraints. The proposed design uses the expected relative size of the contaminated area and the overall sampling rate as the two control variables in determining an optimal sample splitting proportion for a two-stage design. Results are shown through simulation studies and theoretical derivation. Many spatial processes exhibit nonstationary features. We estimate a variance function from a single process observation where the errors are nonstationary and correlated. We assume that the mean process is smooth and that the error process is a product of a smooth variance function and a second-order stationary process. A difference-based approach for a one-dimensional nonstationary process is developed along with a bandwidth selection method which takes into account the error dependence structure. The asymptotic properties of the estimator are investigated, and the estimation results are compared to that of a local-likelihood approach proposed by Anderes and Stein (2011). Simulation study shows that our method has a smaller integrated MSE, fixes the boundary bias problem, and requires far less computing time as the evaluation of likelihood with matrix inversion is not necessary. For a two-dimensional nonstationary process with correlated errors there are a few practical guides for selecting a difference filter of its shape, scale, and weight depending on the degree of correlation in the data. When the data is strongly correlated, a symmetric weighting scheme is preferred; and when the data is weakly correlated or independent, the Hall-Kay-Titterington (1991) weight is preferred. Also a compact filter would minimize introducing bias. The best filter configuration is a three-node line configuration with directional rotation and averaging

Aeronautical engineering: A continuing bibliography with indexes (supplement 289)

This bibliography lists 792 reports, articles, and other documents introduced into the NASA scientific and technical information system in Mar. 1993. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics