Comments on “Improvement of generalized difference-based mixed Liu estimator in partially linear model”

Abstract

We make some comments about the article of Wu (2018 Wu, J. B. 2018. Improvement of generalized difference-based mixed Liu estimator in partially linear model. Communications in Statistics: Theory and Methods 47 (18):4433–42.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and correct the theorems in that article.     

尺度重双正交紧支撑多小波的构造

研究了多小波的构造算法,利用多分辨分析和双正交理论,给出了尺度重双正交多小波;再结合矩阵理论,得到双正交多小波的两尺度矩阵序列;最后通过矩阵的正交扩充给出了一种构造尺度重紧双正交支撑多小波的算法。     

Degree-like centrality with structural zeroes or ones: When is a neighbor not a neighbor?

In the field of social network analysis, there are situations in which researchers hope to ignore certain dyads in the computation of centrality to avoid biased or misleading results, but simply deleting these dyads will result in wrong conclusions. There is little work considering this particular problem except the eigenvector-like centrality method presented in 2015. In this paper, we revisit this problem and present a new degree-like centrality method which also allows some dyads to be excluded in the calculations. This new method adopts the technique of weighted symmetric nonnegative matrix factorization (abbreviated as WSNMF), and we will show that it can be seen as the generalized version of the existing eigenvector-like centrality. After applying it to several data sets, we test this new method's efficiency.     

基于环境社会核算矩阵的内蒙古环境治理投入与经济发展的实证研究

环境治理投入对区域经济各部门的反馈作用及内在联系是环境经济研究的最新领域也是前沿。本文基于内蒙古环境社会核算矩阵(ESAM),利用SAM乘数分析方法实证研究了环境治理投入与经济产出及结构之间的关系。结果表明:①环境治理投入对经济发展具有弱乘数效应;②环境治理投入对环境承载力的提高有正效应;③经济发展对环境自我净化能力有负效应;④第三产业乘数效应弱于第二产业,应加强产业结构优化。其结论可为地区环境政策制定及环境综合治理提供理论依据。     

对Hurwitz定理的一个推广

本文对判别实二次型正定性的重要方法之一———Hurwitz定理做了推广 ,使得本来需从实二次型的矩阵A =(aij) n×n(A′ =A)的左上角元a11开始取从 1到n阶顺序主子式进行的判定 ,变成可以从A的主对角线上任意元aii(i =1,2 ,… ,n)开始取从 1到n阶连序主子式进行判定。因此 ,本文给出的方法使用起来更为方便、灵活 ,具有一定的实用价值     

Tractable Bayesian learning of tree belief networks

In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and can be completely determined analytically in polynomial time. Our result is the first where computing the normalization constant and averaging over a super-exponential number of graph structures can be performed in polynomial time. This follows from two main results: First, we show that factored distributions over spanning trees in a graph can be integrated in closed form. Second, we examine priors over tree parameters and show that a set of assumptions similar to Heckerman, Geiger and Chickering (1995) constrain the tree parameter priors to be a compactly parametrized product of Dirichlet distributions. Besides allowing for exact Bayesian learning, these results permit us to formulate a new class of tractable latent variable models in which the likelihood of a data point is computed through an ensemble average over tree structures.     

Phase Type Distributions with Finite Support

This research is motivated by the fact that many random variables of practical interest have a finite support. For fixed a < b, we consider the distribution of a random variable X = (a + Ymod(b ? a)), where Y is a phase type (PH) random variable. We demonstrate that as we traverse for Y the entire set of PH distributions (or even any subset thereof like Coxian that is dense in the class of distributions on [0, ∞)), we obtain a class of matrix exponential distributions dense in (a, b). We call these Finite Support Phase Type Distributions (FSPH) of the first kind. A simple example shows that though dense, this class by itself is not very efficient for modeling; therefore, we introduce (and derive the EM algorithms for) two other classes of finite support phase type distributions (FSPH). The properties of denseness, connection to Markov chains, the EM algorithm, and ability to exploit matrix-based computations should all make these classes of distributions attractive not only for applied probability but also for a much wider variety of fields using statistical methodologies.     

A New Policy Evaluation Algorithm for Markov Decision Processes with Quasi Birth-Death Structure

ABSTRACT

This paper describes a new algorithm for policy evaluation for Markov decision processes (MDP) that possess a quasi birth-death structure. The proposed algorithm is based on matrix analytic methods which use probabilistic concepts associated with restricting the underlying Markov process to certain state subsets. A telecommunications application example shows that the method offers significant computational reduction compared to a standard MDP policy evaluation approach.     

Analysis of Stochastic Online Bin Packing Processes

Abstract

A stochastic online version of the classical bin packing problem, where a bin corresponds to the capacity of a resource allocated among streams of requests at discrete time units, is a fundamental problem that arises in a wide variety of application areas including bandwidth allocation in networks, memory management in computers, and message transmission in slotted network channels. We derive a mathematical analysis of the corresponding multi-dimensional stochastic process, potentially infinite in each dimension, under a general class of scheduling policies based on a combination of a Lyapunov function technique and matrix-analytic methods. Our analysis yields stability conditions and stationary distributions for this stochastic bin packing process under general probability distributions. We further provide some algorithmic techniques for the numerical computation of these measures.