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

Robust Estimators in Generalized Pareto Models

This paper deals with optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have in mind is calculation of the regulatory capital required by Basel II for a bank to cover operational risk. In this context the tail behavior of the underlying distribution is crucial. This is where extreme value theory enters, suggesting to estimate these high quantiles parameterically using, e.g. GPDs. Robust statistics in this context offers procedures bounding the influence of single observations, so provides reliable inference in the presence of moderate deviations from the distributional model assumptions, respectively from the mechanisms underlying the PBHT.Comment: 26pages, 6 figure

Yet another breakdown point notion: EFSBP - illustrated at scale-shape models

The breakdown point in its different variants is one of the central notions to quantify the global robustness of a procedure. We propose a simple supplementary variant which is useful in situations where we have no obvious or only partial equivariance: Extending the Donoho and Huber(1983) Finite Sample Breakdown Point, we propose the Expected Finite Sample Breakdown Point to produce less configuration-dependent values while still preserving the finite sample aspect of the former definition. We apply this notion for joint estimation of scale and shape (with only scale-equivariance available), exemplified for generalized Pareto, generalized extreme value, Weibull, and Gamma distributions. In these settings, we are interested in highly-robust, easy-to-compute initial estimators; to this end we study Pickands-type and Location-Dispersion-type estimators and compute their respective breakdown points.Comment: 21 pages, 4 figure

Infinitesimally Robust Estimation in General Smoothly Parametrized Models

We describe the shrinking neighborhood approach of Robust Statistics, which applies to general smoothly parametrized models, especially, exponential families. Equal generality is achieved by object oriented implementation of the optimally robust estimators. We evaluate the estimates on real datasets from literature by means of our R packages ROptEst and RobLox

Induction of apoptosis in host cells: a survival mechanism for Leishmania parasites?

Leishmania parasites invade host macrophages, causing infections that are either limited to skin or spread to internal organs. In this study, 3 species causing cutaneous leishmaniasis, L. major, L. aethiopica and L. tropica, were tested for their ability to interfere with apoptosis in host macrophages in 2 different lines of human monocyte-derived macrophages (cell lines THP-1 and U937) and the results confirmed in peripheral blood mononuclear cells (PBMC). All 3 species induced early apoptosis 48 h after infection (expression of phosphatidyl serine on the outer membrane). There were significant increases in the percentage of apoptotic cells both for U937 and PBMC following infection with each of the 3 species. Early apoptotic events were confirmed by mitochondrial membrane permeabilization detection and caspase activation 48 and 72 h after infection. Moreover, the percentage of infected THP-1 and U937 macrophages increased significantly (up to 100%) following treatment with an apoptosis inducer. Since phosphatidyl serine externalization on apoptosing cells acts as a signal for engulfment by macrophages, induction of apoptosis in the parasitized cells could actively participate in spreading the infection. In summary, parasite-containing apoptotic bodies with intact membranes could be released and phagocytosed by uninfected macrophages

Importance Sampling and Stratification for Copula Models

An importance sampling approach for sampling from copula models is introduced. The proposed algorithm improves Monte Carlo estimators when the functional of interest depends mainly on the behaviour of the underlying random vector when at least one of its components is large. Such problems often arise from dependence models in finance and insurance. The importance sampling framework we propose is particularly easy to implement for Archimedean copulas. We also show how the proposal distribution of our algorithm can be optimized by making a connection with stratified sampling. In a case study inspired by a typical insurance application, we obtain variance reduction factors sometimes larger than 1000 in comparison to standard Monte Carlo estimators when both importance sampling and quasi-Monte Carlo methods are used.NSERC, Grant 238959 NSERC, Grant 501

Antimicrobial Peptides and Skin: A Paradigm of Translational Medicine

Antimicrobial peptides (AMPs) are small, cationic, amphiphilic peptides with broad-spectrum microbicidal activity against both bacteria and fungi. In mammals, AMPs form the first line of host defense against infections and generally play an important role as effector agents of the innate immune system. The AMP era was born more than 6 decades ago when the first cationic cyclic peptide antibiotics, namely polymyxins and tyrothricin, found their way into clinical use. Due to the good clinical experience in the treatment of, for example, infections of mucus membranes as well as the subsequent understanding of mode of action, AMPs are now considered for treatment of inflammatory skin diseases and for improving healing of infected wounds. Based on the preclinical findings, including pathobiochemistry and molecular medicine, targeted therapy strategies are developed and first results indicate that AMPs influence processes of diseased skin. Importantly, in contrast to other antibiotics, AMPs do not seem to propagate the development of antibiotic-resistant micro-organisms. Therefore, AMPs should be tested in clinical trials for their efficacy and tolerability in inflammatory skin diseases and chronic wounds. Apart from possible fields of application, these peptides appear suited as an example of the paradigm of translational medicine for skin diseases which is today seen as a `two-way road' - from bench to bedside and backwards from bedside to bench. Copyright (c) 2012 S. Karger AG, Base