矩阵不等式AX≥B的一类反问题及其最佳逼近

讨论如下两个问题： 问题Ⅰ　给定非零向量Ｘ∈Ｒｎ,Ｂ∈Ｒｍ,求矩阵Ａ∈Ｒｍ×ｎ使得ＡＸ≥Ｂ． 问题Ⅱ　给定Ａ∈Ｒｍ×ｎ,求矩阵Ａ∈ＳＡ,使得 其中是Ｆｒｏｂｅｎｉｕｓ范数,ＳＡ表示问题Ⅰ的解集合。 给出了ＳＡ一般形式,对于问题Ⅱ,给出了解的表达式及一个数值例子。     

The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval

A new two-parameter distribution over the unit interval, called the Unit-Inverse Gaussian distribution, is introduced and studied in detail. The proposed distribution shares many properties with other known distributions on the unit interval, such as Beta, Johnson S_B, Unit-Gamma, and Kumaraswamy distributions. Estimation of the parameters of the proposed distribution are obtained by transforming the data to the inverse Gaussian distribution. Unlike most distributions on the unit interval, the maximum likelihood or method of moments estimators of the parameters of the proposed distribution are expressed in simple closed forms which do not need iterative methods to compute. Application of the proposed distribution to a real data set shows better fit than many known two-parameter distributions on the unit interval.     

New bivariate gamma types with MIMO application

In this paper a bivariate gamma type distribution emanating from the diagonal elements of an inverse Wishart type distribution is developed; which in turn originates from the complex matrix variate elliptical class. From this, a bivariate Weibullised gamma type distribution is also presented, of which the bivariate Nakagami-m type is a special case. The derived results may be applied as decision statistics for a MIMO (multiple input multiple output) system with two transmit antennas. It is proposed that under this elliptical umbrella some performance measures such as the outage probability of MIMO systems can be analyzed in broad generality.     

Conjugate analysis of multivariate normal data with incomplete observations

The authors discuss prior distributions that are conjugate to the multivariate normal likelihood when some of the observations are incomplete. They present a general class of priors for incorporating information about unidentified parameters in the covariance matrix. They analyze the special case of monotone patterns of missing data, providing an explicit recursive form for the posterior distribution resulting from a conjugate prior distribution. They develop an importance sampling and a Gibbs sampling approach to sample from a general posterior distribution and compare the two methods.     

Exact Distributional Results for Random Resistance Trees

With a view to the study of, for instance, arterial trees, this paper presents some exact distributional results on finite trees with (reciprocal) inverse Gaussian and gamma resistances. In particular, it is shown that under the specified model the conditional distribution of the minimal sufficient statistic given the total resistance of the tree is a convolution of gamma distributions and two-dimensional reciprocal inverse Gaussian distributions.     

Time-varying coefficient cumulative gap time models for intensive longitudinal ecological momentary assessment data with missingness

Ecological momentary assessment (EMA) studies investigate intensive repeated observations of the current behavior and experiences of subjects in real time. In particular, such studies aim to minimize recall bias and maximize ecological validity, thereby strengthening the investigation and inference of microprocesses that influence behavior in real-world contexts by gathering intensive information on the temporal patterning of behavior of study subjects. Throughout this paper, we focus on the data analysis of an EMA study that examined behavior of intermittent smokers (ITS). Specifically, we sought to explore the pattern of clustered smoking behavior of ITS, or smoking ‘bouts’, as well as the covariates that predict such smoking behavior. To do this, in this paper we introduce a framework for characterizing the temporal behavior of ITS via the functions of event gap time to distinguish the smoking bouts. We used the time-varying coefficient models for the cumulative log gap time and to characterize the temporal patterns of smoking behavior, while simultaneously adjusting for behavioral covariates, and incorporated the inverse probability weighting into the models to accommodate missing data. Simulation studies showed that irrespective of whether missing by design or missing at random, the model was able to reliably determine prespecified time-varying functional forms of a given covariate coefficient, provided the the within-subject level was small.     

Inverse power Maxwell distribution: statistical properties,estimation and application

In this paper, we introduced a new probability distribution named as inverse power Maxwell distribution. The proposal distribution can be seen as an extension of the Maxwell distribution with more flexibility in modeling upside-down lifetime data. Some statistical properties of this distribution are derived. In estimation viewpoint, five methods are used for estimating the unknown parameters of the distribution and these methods are performed through the simulation study. Finally, two real data sets were analyzed to illustrate the applicability of the proposed distribution, proving that it fits each real data set much better than some other existing distributions.     

进城农民教育和工作经验对收入倒“U”型影响的检验

进城农民群体被看做是缩小城乡收入差距、促进社会和谐发展的关键群体,虽然相关研究深化了有关进城农民劳动力收入决定因素的认识,但是,针对教育和工作经验对中国进城农民收入影响的研究较少,且缺乏对影响是否持续呈线性的研究。基于明瑟扩展方程,结合典型地区数据,分析发现教育和工作经验对进城农民收入具有显著的正向影响,工作经验与收入之间存在倒"U"型关系,而教育与收入之间不存在倒"U"型关系。在分析结论的基础上提出了完善进城农民教育和培训体系等建议。     

Fuzzy矩阵广义逆阵的一个应用

本文利用Fuzzy矩阵广义逆阵的理论讨论了Fuzzy矩阵方程何时有解的问题,并给出了几个相应的结论．     

Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods1

We investigate a class of semiparametric ARCH(∞) models that includes as a special case the partially nonparametric (PNP) model introduced by Engle and Ng (1993) and which allows for both flexible dynamics and flexible function form with regard to the “news impact” function. We show that the functional part of the model satisfies a type II linear integral equation and give simple conditions under which there is a unique solution. We propose an estimation method that is based on kernel smoothing and profiled likelihood. We establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model. We also discuss efficiency of both the parametric part and the nonparametric part. We investigate the performance of our procedures on simulated data and on a sample of S&P500 index returns. We find evidence of asymmetric news impact functions, consistent with the parametric analysis.