Multivariate Discrete Distributions with a Product-Type Dependence

A discrete multivariate probability distribution for dependent random variables, which contains the Poisson and Geometric conditionals distributions as particular cases, is characterized by means of conditional expectations of arbitrary one-to-one functions. Independence of the random variables is also characterized in terms of these conditional expectations. For certain exchangeable and partially exchangeable random variables with a joint distribution of this form it is shown that maximum likelihood estimates coincide with the simple method of moments estimates, suggesting that these models offer a pragmatic way to analyze certain dependent data.     

Effect of Data Transformations on Predictive Risk Indicators

Risk indicators used in many applications usually involve certain transformations of the variables of interest, such as averages or maxima over given time periods or spatial regions, threshold exceedances, etc., or a combination of them. A common practice is to predict these indicators by applying the same type of transformation on the sample data, that is, the ??historical?? values of the same indicators are used as the sample information set. In this work, the loss of information derived from the transformations defining the sample set is studied for different indicators and considering a flexible covariance model separating fractal dimension and memory. The evaluations and comparisons are performed in terms of predictive mutual information based on Shannon??s entropy. The results obtained for different scenarios suggest that, depending on the type of risk indicator considered and the dependence structure of the process of interest, the changes in terms of predictive information using diverse transformations of the observations may be substantial.     

Dependence Properties of Multivariate Mixture Distributions and Their Applications

Consider a multivariate mixture model where the random variables X ₁, ..., X _n given (₁, ..., _n ), are conditionally independent. Conditions are obtained under which different kinds of positive dependence hold among X _i 's. The results obtained are applied to a variety of problems including the concomitants of order statistics and of record values; and to frailty models.     

Tail Risk of Multivariate Regular Variation

Tail risk refers to the risk associated with extreme values and is often affected by extremal dependence among multivariate extremes. Multivariate tail risk, as measured by a coherent risk measure of tail conditional expectation, is analyzed for multivariate regularly varying distributions. Asymptotic expressions for tail risk are established in terms of the intensity measure that characterizes multivariate regular variation. Tractable bounds for tail risk are derived in terms of the tail dependence function that describes extremal dependence. Various examples involving Archimedean copulas are presented to illustrate the results and quality of the bounds.     

Non-Parametric Estimation of the Limit Dependence Function of Multivariate Extremes

This paper presents a new estimation procedure for the limit distribution of the maximum of a multivariate random sample. This procedure relies on a new and simple relationship between the copula of the underlying multivariate distribution function and the dependence function of its maximum attractor. The obtained characterization is then used to define a class of kernel-based estimates for the dependence function of the maximum attractor. The consistency and the asymptotic distribution of these estimates are considered.     

在某些正则区域上的多元B形式曲面

本文首先通过在多面体区域上抬高维数的技巧给出了多元Ｂ形式中曲面的一般性定义．由此我们构造了平行四边形域上、正六边形域上和正八边形成上Ｂ形式的同次曲面格式，并给出了其基函数的递推公式和求导公式．同时我们也给出了正六边形域上插值角点的Ｂ形式同次曲面的表示式．     

Dependence Relations Among the Shifts of a Multivariate Refinable Distribution

Refinable functions are an intrinsic part of subdivision schemes and wavelet constructions. The relevant properties of such functions must usually be determined from their refinement masks. In this paper, we provide a characterization of linear independence for the shifts of a multivariate refinable vector of distributions in terms of its (finitely supported) refinement mask. March 14, 1998. Dates revised: February 3, 1999 and August 6, 1999. Date accepted: November 16, 1999.     

一类嵌套多元指数分布相关参数的矩型估计

本文研究一类具有三个相关参数的嵌套多元指数分布,其生存函数为其中,0相似文献   

Dealing with Dependence in Risk Simulations

Journal of the Operational Research Society - Difficulties arise in choosing a suitable sampling scheme for risk simulations when variables are not judged to be independent of each other. This...     

MM Algorithms for Some Discrete Multivariate Distributions

The MM (minorization–maximization) principle is a versatile tool for constructing optimization algorithms. Every EM algorithm is an MM algorithm but not vice versa. This article derives MM algorithms for maximum likelihood estimation with discrete multivariate distributions such as the Dirichlet-multinomial and Connor–Mosimann distributions, the Neerchal–Morel distribution, the negative-multinomial distribution, certain distributions on partitions, and zero-truncated and zero-inflated distributions. These MM algorithms increase the likelihood at each iteration and reliably converge to the maximum from well-chosen initial values. Because they involve no matrix inversion, the algorithms are especially pertinent to high-dimensional problems. To illustrate the performance of the MM algorithms, we compare them to Newton’s method on data used to classify handwritten digits.     

Study of Dependence for Some Stochastic Processes

Abstract

This article is concerned with studying the following problem: Consider a multivariate stochastic process whose law is characterized in terms of some infinitesimal characteristics, such as the infinitesimal generator in case of finite Markov chains. Under what conditions imposed on these infinitesimal characteristics of this multivariate process, the univariate components of the process agree in law with given univariate stochastic processes. Thus, in a sense, we study a stochastic processe' counterpart of the stochastic dependence problem, which in case of real valued random variables is solved in terms of Sklar's theorem.     

基于情景分析的多维拟凸风险统计量

本文定义了三类特殊的多维风险统计量,分别是多维共单调拟凸风险统计量、多维拟凸风险统计量和多维经验分布不变拟凸风险统计量,并采用对偶方法给出了它们的表示定理.本文的结果既是一维拟凸风险统计量的推广,也是多维凸风险统计量的拓展.     

随机波动率模型下技术分析指标的一些性质(英文)

一些流行的技术指标(例如布林带,RSI,ROC等)被股市交易者广为使用.交易者将每日(小时,周,……)的实际股价作为计算某个技术指标的样本,通过观察相关频率来指导投资.技术指标的有效性已在广泛的应用中得到了验证.我们已经证明在Black-Scholes模型下,某些技术指标有许多有用的统计性质.作为更一般的情况,随机波动率模型在金融数学中得到了广泛的讨论.本文基于随机波动率模型对技术指标的统计性质进行了研究.研究结果表明,如果股票价格服从随机波动率模型,则技术指标的合理性可以得到有力的证明,从这个角度我们为技术分析奠定理论基础.     

Dependence Estimation and Visualization in Multivariate Extremes with Applications to Financial Data

We investigate extreme dependence in a multivariate setting with special emphasis on financial applications. We introduce a new dependence function which allows us to capture the complete extreme dependence structure and present a nonparametric estimation procedure. The new dependence function is compared with existing measures including the spectral measure and other devices measuring extreme dependence. We also apply our method to a financial data set of zero coupon swap rates and estimate the extreme dependence in the data.AMS 2000 Subject Classification. Primary—62G32, 62H12 Secondary—62E20     

Some Classes of Multivariate Life Distributions in Discrete Time

New classes of multivariate survival distribution functions based on monotonic behaviour of a multivariate failure rate are developed in the discrete set up. Relationship among the classes along with multivariate geometric distributions that act as boundaries of the various classes are identified.     

多元部分线性模型的几个渐近性质(英文)

The paper considers a multivariate partially linear model under independent errors,and investigates the asymptotic bias and variance-covariance for parametric component βand nonparametric component F（·）by the GJS estimator and Kernel estimation.     

Some Basic Extensions of Gustafson-Rakha's Multivariate Basic Hypergeometric Series

In this paper we extend some special cases of the multivariate basic hypergeometric series associated to the roots system of type A_m A_m that has been established and proved in [8]. For both types of the series, we will prove that when m = 2n; n = 1 m = 2n; n =1 one of the series is equivalent to Jackson's ₈ Y₇ _8 \Psi _7 sum, while the other series is equivalent to the basic Gauss' sum.