Extreme value properties of multivariate t copulas

The extremal dependence behavior of t copulas is examined and their extreme value limiting copulas, called the t-EV copulas, are derived explicitly using tail dependence functions. As two special cases, the Hüsler–Reiss and the Marshall–Olkin distributions emerge as limits of the t-EV copula as the degrees of freedom go to infinity and zero respectively. The t copula and its extremal variants attain a wide range in the set of bivariate tail dependence parameters. Supported by NSERC Discovery Grant.     

多变量极值理论在银行操作风险度量中的运用

针对银行操作风险损失分布的厚尾性和损失事件之间的尾部相依性,首先用单变量极值理论建立了单个损失事件计量模型,然后用多变量极值的连接函数反映了损失事件之间的尾部相依性,避免了计量中对银行操作风险的低估和对监管资本要求高估.     

极值理论在风险度量中的应用--基于上证180指数

精确度量风险是金融风险管理的关键问题。本引入广义帕雷托分布代替传统的正态分布等，精确描述金融收益的厚尾特征。并将基于广义帕雷托分布的VaR模型和其它模型方法，如GARCH(1，1)、GARCH(1，1)-t、历史模拟法、方差-协方差方法，进行比较分析。实证研究表明，基于广义帕雷托分布的VaR模型比传统的模型方法更适合厚尾分布高分位点的预测，并且其预测结果比较稳定。这使得基于广义帕雷托分布的VaR模型成为VaR度量方法中最稳健的方法之一。     

The approximation of logarithmic function by q-Bernstein polynomials in the case q > 1

Since in the case q > 1, q-Bernstein polynomials are not positive linear operators on C[0,1], the study of their approximation properties is essentially more difficult than that for 0<q<1. Despite the intensive research conducted in the area lately, the problem of describing the class of functions in C[0,1] uniformly approximated by their q-Bernstein polynomials (q > 1) remains open. It is known that the approximation occurs for functions admit ting an analytic continuation into a disc {z:|z| < R}, R > 1. For functions without such an assumption, no general results on approximation are available. In this paper, it is shown that the function f(x) = ln (x + a), a > 0, is uniformly approximated by its q-Bernstein polynomials (q > 1) on the interval [0,1] if and only if a ≥ 1.      

应用极值理论计算VaR的一种方法

在险价值(value at risk，简称VaR)是度量市场风险的一种普遍使用的工具，也是金融风险管理中的基础工具。计算VaR有许多不同的方法，本考虑了数据间的相关性，通过部分重叠数据分组的方法来计算VaR，发现所得到的VaR更符合实际；另外，我们对分组大小作了研究，发现分组数据大小的幂律存在，并对恒生指数作了具体分析。由此得出计算VaR的合理的数据分组大小。     

The sharpness of convergence results for <Emphasis Type="Italic">q</Emphasis>-Bernstein polynomials in the case <Emphasis Type="Italic">q</Emphasis> > 1

Due to the fact that in the case q > 1 the q-Bernstein polynomials are no longer positive linear operators on C[0, 1], the study of their convergence properties turns out to be essentially more difficult than that for q < 1. In this paper, new saturation theorems related to the convergence of q-Bernstein polynomials in the case q > 1 are proved.     

用蒙特卡罗方法求取广义线性混合模型之最大似然估计:应用于求取乳癌死亡率之小区域估计

本文使用蒙特卡罗方法, 求得广义线性混合模型之最大似然估计, 并提供用来评估统计参数之收敛和精确度之实用方法\bd 仿真研究显示无偏之固定效应参数估计, 而方差分量估计之误差则相近于前人结果\bd 应用举例为使用泊松分布求取乳癌死亡率之小区域估计.     

Estimation of parameters in the discrete distributions of order k

This paper considers estimating parameters in the discrete distributions of order k such as the binomial, the geometric, the Poisson and the logarithmic series distributions of order k. It is discussed how to calculate maximum likelihood estimates of parameters of the distributions based on independent observations. Further, asymptotic properties of estimators by the method of moments are investigated. In some cases, it is found that the values of asymptotic efficiency of the moment estimators are surprisingly close to one.     

On the Maximum Number of Cliques in a Graph

A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) graphs with n vertices and m edges; (2) graphs with n vertices, m edges, and maximum degree Δ; (3) d-degenerate graphs with n vertices and m edges; (4) planar graphs with n vertices and m edges; and (5) graphs with n vertices and no K₅-minor or no K_3,3-minor. For example, the maximum number of cliques in a planar graph with n vertices is 8(n − 2). Research supported by a Marie Curie Fellowship of the European Community under contract 023865, and by the projects MCYT-FEDER BFM2003-00368 and Gen. Cat 2001SGR00224.     

Metrization of Epi-Convergence: An Application to the Strong Consistency of M-Estimators

Strong consistency in the class of M-estimators is examined here as an application of epi-convergence, a functional convergence which is particularly suited for the study of convergence of the functions' minimizing values and arguments. Starting from a 1988 paper by J. Dupaova and R. Wets, which contains a thorough account of the relations between consistency and epi-convergence, a quantitative approach of the same topic is pursued here. Epi-convergence is compared with two definitions introduced in 1980 by one of the authors. The results are merged in order to define a distance between lower semicontinuous functions that is compatible with epi-convergence and bounds the distance between the minimizing arguments. These results applied to the statistical problem allow the definition of a bound of the distance between the estimator and the parameter.     

Characterization of Two-Scale Gradient Young Measures and Application to Homogenization

This work is devoted to the study of two-scale gradient Young measures naturally arising in nonlinear elasticity homogenization problems. Precisely, a characterization of this class of measures is derived and an integral representation formula for homogenized energies, whose integrands satisfy very weak regularity assumptions, is obtained in terms of two-scale gradient Young measures.     

THE CONSTRUCTION OF DENUMERABLE q-PROCESSES IN RANDOM ENVIRONMENTS SATISFYING （F） OR （B）

This article is a continuation of[9].Based on the discussion of random Kolmogorov forward（backward）equations,for any given q-matrix in random environment, Q（θ）=（q（θ;x,y）,x,y∈X）,an infinite class of q-processes in random environments satisfying the random Kolmogorov forward（backward）equation is constructed.Moreover, under some conditions,all the q-processes in random environments satisfying the random Kolmogorov forward（backward）equation are constructed.     

On the Wl q-Regularity of Solutions to Systems of Differential Equations in the Case When the Equations Are Constructed from Discontinuous Functions

Some solution, final in a sense from the standpoint of the theory of Sobolev spaces, is obtained to the problem of regularity of solutions to a system of (generally) nonlinear partial differential equations in the case when the system is locally close to elliptic systems of linear equations with constant coefficients. The main consequences of this result are Theorems 5 and 8. According to the first of them, the higher derivatives of an elliptic C ^l -smooth solution to a system of lth-order nonlinear partial differential equations constructed from C ^l -smooth functions meet the local Hoelder condition with every exponent , 0<<1. Theorem 8 claims that if a system of linear partial differential equations of order l with measurable coefficients and right-hand sides is uniformly elliptic then, under the hypothesis of a (sufficiently) slow variation of its leading coefficients, the degree of local integrability of lth-order partial derivatives of every W ^l _q,loc-solution, q>1, to the system coincides with the degree of local integrability of lower coefficients and right-hand sides.     

Inference in lognormal multidimensional diffusion processes with exogenous factors: Application to modelling in economics

The multidimensional lognormal diffusion process with exogenous factors is treated using the Kolmogorov equations, and the mean vector and covariance matrix are estimated using discrete sampling by the maximum-likelihood method. Also, this process is constructed as a solution of a multidimensional stochastic differential equation, and an estimation is made through the maximum-likelihood method to infer the parameters of the exogenous factors, this time using continuous sampling. Finally, a test for a hypothesis based on these parameters is constructed.     

The Method of Upper and Lower Solutions for a Lidstone Boundary Value Problem

In this paper we develop the monotone method in the presence of upper and lower solutions for the 2nd order Lidstone boundary value problem

Estimation of elastic parameters in beams and certain plates:H 1 regularization

The estimation of elastic parameters in beams and certain types of plates is discussed using anH ¹-regularization technique that easily accommodates pointwise constraints. The optimal coefficient is shown to enjoy more regularity than that assumed in the formulation of the problem. This additional smoothness is useful for analyzing the limit behavior of finite-dimensional problems. Numerical results are presented.This work was supported in part by the Air Force Office of Scientific Research, Grant AFOSR-84-0271.     

The Borel regulator map on pictures, II: An example from Morse theory

By doing parametrized Morse theory on circle bundles overS ², we produce pictures representing elements ofK ₃ of cyclotomic number fields. By computing the regulator map on these pictures, we show that they are rationally nontrivial.Research supported by NSF Grant No. MCS-90-02512.     

An application of Bayesian (ABIC) smoothing methods to estimating space and time variations in the magnitude distributions of earthquakes

On the basis of Akaike's Bayesian information criterion (ABIC), a new method of estimating temporal and spacial variations in the magnitude-frequency relation (b value) is developed. The space-time volume studied is divided into a number of segments having equal volume, for which b values are estimated. The smoothness of the estimated b value is guaranteed by the introduction of a prior distribution. The parameters of the prior distribution are chosen in such a way as to minimize the ABIC. This method is employed to study the temporal and spatial variations of b values for microearthquake activity in the Kanto, Tokai and Tottori areas, where seven earthquakes having magnitudes of M6.0 and larger have recently taken place. States of temporal variations of b values are classified into three groups; increase, decrease and nochange. The space-time volume of decrease accounts for approximately 10% of the total volume. For a period before the occurrence of earthquakes, the decrease appears more frequently than might be expected. It is concluded that the decrease in the b value is a promising candidate to act as a precursory phenomena.This work was carried out under the ISM Cooperative Research Program (88-ISM CRP-60).     

The polynomial degree of the Grassmannian G(1,n,q) of lines in finite projective space PG(n, q)

Let G: = G(1,n,q) denote the Grassmannian of lines in PG(n,q), embedded as a point-set in PG(N, q) with For n = 2 or 3 the characteristic function of the complement of G is contained in the linear code generated by characteristic functions of complements of n-flats in PG(N, q). In this paper we prove this to be true for all cases (n, q) with q = 2 and we conjecture this to be true for all remaining cases (n, q). We show that the exact polynomial degree of is for δ: = δ(n, q) = 0 or 1, and that the possibility δ = 1 is ruled out if the above conjecture is true. The result deg( for the binary cases (n,2) can be used to construct quantum codes by intersecting G with subspaces of dimension at least      

基于不确定测度及积分的民航空管运行风险决策模型研究

以往民航空管安全管理中,大多对单一类型威胁或差错进行评估以管理风险,忽略了威胁与差错之间的交互作用,难以准确反映出不同类型风险之间的相关性。本文提出了基于不确定测度的空管运行风险决策模型,即将不确定积分Choquet积分作为风险函数,在由威胁和差错构成的集合的概念下,由Shapley值作为校正函数,重新评估各个威胁和差错的风险值。本文通过应用上述风险决策模型,结合案例得出了考虑交互作用的空管运行修正风险值,该风险值与单一风险值相比更贴近空管运行实际情况,因而对风险决策更具指导意义。