Reduced-bias estimator of the Conditional Tail Expectation of heavy-tailed distributions

International audienceSeveral risk measures have been proposed in the literature. In this paper, we focus on the estimation of the Conditional Tail Expectation (CTE). Its asymptotic normality has been first established in the literature under the classical assumption that the second moment of the loss variable is finite, this condition being very restrictive in practical applications. Such a result has been extended by Necir {\it et al.} (2010) in the case of infinite second moment. In this framework, we propose a reduced-bias estimator of the CTE. We illustrate the efficiency of our approach on a small simulation study and a real data analysis

Analysis causes of the incidence and compare social, economic, physical characteristics of informal settlements, case study: city of Marivan in Kurdistan province

Informal settlements are one of the problems of urban management in developing countries. Various theories about the causes and management of these settlements have been proposed. The most important of these theories, new socialist, liberal and dependency can be noted. The theory that argues for mandatory clearing informal settlement is not logical. Empowerment approach to be interested by countries and international organizations, and successful examples of this approach, with emphasis on the internal dynamics of these communities has been experienced. This paper tries to analyze the causes of marginalization and social, economic and spatial characteristics of informal settlement of Marivan city in Kurdistan province. Research areas consist of 4 region of Marivan informal settlement (Kosar,tape Mosk, sardoshiha, Tefine) sample size based on Cochran formula is 320 samples that Randomly and in four districts have been selected. Reasons for residents that they living in such places and social, economic characteristics of marginalized communities collected and entered into SPSS software and have been analyzed. The results show that more than 50 percent of residents in informal settlement areas of the city have come to this neighborhood. The main factor in the development of these four areas is not rural migrants. The highest levels of rural migrants from the neighborhood Tefin are that only 47% of residents are immigrants. The results suggest the great differences in social, economic and physical characteristics of slums. Among neighborhoods communities tapa Mosk and Tefini in the index close to each other and compare to two other neighborhoods are poor

Complex Random Energy Model: Zeros and Fluctuations

The partition function of the random energy model at inverse temperature $\beta$ is a sum of random exponentials $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables (= random energies), and $n=\log N$. We study the large $N$ limit of the partition function viewed as an analytic function of the complex variable $\beta$. We identify the asymptotic structure of complex zeros of the partition function confirming and extending predictions made in the theoretical physics literature. We prove limit theorems for the random partition function at complex $\beta$, both on the logarithmic scale and on the level of limiting distributions. Our results cover also the case of the sums of independent identically distributed random exponentials with any given correlations between the real and imaginary parts of the random exponent.Comment: 31 pages, 1 figur

The morphology and biochemistry of nanostructures provide evidence for synthesis and signaling functions in human cerebrospinal fluid

<p>Abstract</p> <p>Background</p> <p>Cerebrospinal fluid (CSF) contacts many brain regions and may mediate humoral signaling distinct from synaptic neurotransmission. However, synthesis and transport mechanisms for such signaling are not defined. The purpose of this study was to investigate whether human CSF contains discrete structures that may enable the regulation of humoral transmission.</p> <p>Methods</p> <p>Lumbar CSF was collected prospectively from 17 participants: with no neurological or psychiatric disease, with Alzheimer's disease, multiple sclerosis, or migraine; and ventricular CSF from two cognitively healthy participants with long-standing shunts for congenital hydrocephalus. Cell-free CSF was subjected to ultracentrifugation to yield supernatants and pellets that were examined by transmission electron microscopy, shotgun protein sequencing, electrophoresis, western blotting, lipid analysis, enzymatic activity assay, and immuno-electron microscopy.</p> <p>Results</p> <p>Over 3,600 CSF proteins were identified from repeated shotgun sequencing of cell-free CSF from two individuals with Alzheimer's disease: 25% of these proteins are normally present in membranes. Abundant nanometer-scaled structures were observed in ultracentrifuged pellets of CSF from all 16 participants examined. The most common structures included synaptic vesicle and exosome components in 30-200 nm spheres and irregular blobs. Much less abundant nanostructures were present that derived from cellular debris. Nanostructure fractions had a unique composition compared to CSF supernatant, richer in omega-3 and phosphoinositide lipids, active prostanoid enzymes, and fibronectin.</p> <p>Conclusion</p> <p>Unique morphology and biochemistry features of abundant and discrete membrane-bound CSF nanostructures are described. Prostaglandin H synthase activity, essential for prostanoid production and previously unknown in CSF, is localized to nanospheres. Considering CSF bulk flow and its circulatory dynamics, we propose that these nanostructures provide signaling mechanisms <it>via </it>volume transmission within the nervous system that are for slower, more diffuse, and of longer duration than synaptic transmission.</p

An analysis of multidimensional contingency talbes

In this thesis we consider the following model for a three-dimensional r ˣ s ˣ t contingency table: [formula omitted]. A dot indicates summation over the replaced subscript. The f[formula omitted]’s represent the frequencies and the P[formula omitted]'s represent the proportions. The problem we are concerned with is testing the hypothesis H₀: [formula omitted] = 0 for all i, j, k. i.e. no second order interaction is present. We then seek to extend the model and problem to a w-way table. We use the method of the likelihood ratio . To assist us in determining the numerator of the likelihood ratio we reformulate a theorem about constrained extrema and Lagrange multipliers and prove this reformulation. Some general conclusions we draw are: there are two extensions to our 3-way model; results we obtain using our model and methods are in close agreement with results obtained using the models and methods of other statisticians.Science, Faculty ofMathematics, Department ofGraduat

Maximum likelihood estimation of stochastic frontier models by the Fourier transform

The paper is concerned with several kinds of stochastic frontier models whose likelihood function is not available in closed form. First, with output-oriented stochastic frontier models whose one-sided errors have a distribution other than the standard ones (exponential or half-normal). The gamma and beta distributions are leading examples. Second, with input-oriented stochastic frontier models which are common in theoretical discussions but not in econometric applications. Third, with two-tiered stochastic frontier models when the one-sided error components follow gamma distributions. Fourth, with latent class models with gamma distributed one-sided error terms. Fifth, with models whose two-sided error component is distributed as stable Paretian and the one-sided error is gamma. The principal aim is to propose approximations to the density of the composed error based on the inversion of the characteristic function (which turns out to be manageable) using the Fourier transform. Procedures that are based on the asymptotic normal form of the log-likelihood function and have arbitrary degrees of asymptotic efficiency are also proposed, implemented and evaluated in connection with output-oriented stochastic frontiers. The new methods are illustrated using data for US commercial banks, electric utilities, and a sample from the National Youth Longitudinal Survey

A Data-Analytic Method for Forecasting Next Record Catastrophe Loss

We develop in this article a data-analytic method to forecast the severity of next record insured loss to property caused by natural catastrophic events. The method requires and employs the knowledge of an expert and accounts for uncertainty in parameter estimation. Both considerations are essential for the task at hand because the available data are typically scarce in extreme value analysis. In addition, we consider three-parameter Gamma priors for the parameter in the model and thus provide simple analytical solutions to several key elements of interest, such as the predictive moments of record value. As a result, the model enables practitioners to gain insights into the behavior of such predictive moments without concerning themselves with the computational issues that are often associated with a complex Bayesian analysis. A data set consisting of catastrophe losses occurring in the United States between 1990 and 1999 is analyzed, and the forecasts of next record loss are made under various prior assumptions. We demonstrate that the proposed method provides more reliable and theoretically sound forecasts, whereas the conditional mean approach, which does not account for either prior information or uncertainty in parameter estimation, may provide inadmissible forecasts. Copyright The Journal of Risk and Insurance.