平方数的位数和函数的渐近分布

设正整数n的二进制展开式为n=∑εi2^i,这里εi=0或1,i≥0,定义二进制位数和函数为s（n）=∑εi.证明了假设n^2的二进制展开式中每个位置上0和1出现的概率相等,则s（n^2）在模2和模3的剩余类里的浙近分布是均匀的．     

基于互反和互补的区间偏好信息集结方法研究

主要研究区间数互反和互补判断矩阵的集结排序方法。在区间数互反和互补判断矩阵概念的基础上,给出了区间数互反和互补判断矩阵的一致性定义。根据一致性的定义,提出了基于线性规划模型的区间数互反和互补判断矩阵集结方法,并通过实例说明了方法的可行性和有效性。     

非流动性市场中的跨期最优消费和投资策略

本文在Merton跨期最优消费和资产组合的理论框架内引入非流动性资产,构造了一个三资产的连续时间经济模型,探讨流动性约束对投资者最优消费和投资决策的影响。本文用动态规划方法给出了跨期优化问题的解析解。数值分析表明对投资者而言,非流动性资产的真实价值低于其市值,必须引入影子价格来刻划这种流动性效应;流动性约束降低了投资者的福利,并且显著地影响到投资者的消费和投资策略。     

面向对象的时序逻辑语言

针对时序逻辑语言缺少面向对象概念的现状,对投影时序逻辑进行了扩展,介绍了新的语法和语义。在扩展投影时序逻辑中,基于变量集合的层次化和谓词的分组,给出了对象、类和继承等概念的形式化定义。扩展投影时序逻辑的一个可执行子集被定义为面向对象的时序逻辑语言FramedTempura++,它能够用于面向对象的程序设计,可以模拟组合Web服务的执行。所给出的实例表明,该语言与FramedTempura相比,能有效地重用代码,提高了代码的可读性和可维护性。     

基于Normal Form理论的电力系统3阶解析解

在对电力系统动态方程进行泰勒级数展开的基础上,运用normal form理论推导出其3阶解析解。分别对单机无穷大系统和2区域4机系统进行了仿真,通过在时域和频域定义的两个近似度指标对比分析线性解析解,2阶解析解及3阶解析解在分析电力系统受扰后的动态特性精确性。并且应用prony算法对仿真结果进行定量分析,检测到了数值积分解中高阶复合模态的存在。从而,验证了推导的3阶解析解对受扰后系统进行分析的有效性。     

混合所有制改革、产权性质与企业风险变化

加强国有企业混合所有制改革中的风险管控是实施经济结构调整的重要保障之一。选取2000—2015年中国A股上市企业为样本,对不同分类特征下的混合和非混合所有制企业风险水平进行非平衡面板实证比较研究。结果表明:混合所有制企业的系统性风险（Beta系数）和财务风险（Z指数）确实低于非混合所有制企业,但资本市场的回归结果显示,其中混合所有制国有控股企业的风险水平表现相对较低,而混合所有制民营控股企业的风险水平则要高,这说明当企业从非混合向混合国有控股转变,或是在国有企业中引入非国有资本时能够降低企业的经营风险,而当企业从非混合向混合民营控股转变,或是在民营企业中引入国有资本时反而会增加企业的经营风险,但无论是从非混合向混合国有控股转变,还是向混合民营控股转变,企业的收益波动风险都会显著提升。     

Selection of terms in random coefficient regression models

The selection of suitable terms in random coefficient regression models is a challenging problem to practitioners. Although many techniques, ranging from those with a theoretical flavour to those with an exploratory spirit, have been proposed for such purposes, no particular one may be considered as a paradigm. In fact, many authors advocate that they should be used in a complementary way. We consider exploratory methods based on fitting standard regression models to the individual response profiles or to the rows of the sample within-units covariance matrix (for balanced data) that may serve as additional tools in the process of selecting an appropriate model. We evaluate the performance of the proposal via a simulation study and consider applications to two examples in the field of Biostatistics.     

Analyzing clustered count data with a cluster-specific random effect zero-inflated Conway–Maxwell–Poisson distribution

Count data analysis techniques have been developed in biological and medical research areas. In particular, zero-inflated versions of parametric count distributions have been used to model excessive zeros that are often present in these assays. The most common count distributions for analyzing such data are Poisson and negative binomial. However, a Poisson distribution can only handle equidispersed data and a negative binomial distribution can only cope with overdispersion. However, a Conway–Maxwell–Poisson (CMP) distribution [4] can handle a wide range of dispersion. We show, with an illustrative data set on next-generation sequencing of maize hybrids, that both underdispersion and overdispersion can be present in genomic data. Furthermore, the maize data set consists of clustered observations and, therefore, we develop inference procedures for a zero-inflated CMP regression that incorporates a cluster-specific random effect term. Unlike the Gaussian models, the underlying likelihood is computationally challenging. We use a numerical approximation via a Gaussian quadrature to circumvent this issue. A test for checking zero-inflation has also been developed in our setting. Finite sample properties of our estimators and test have been investigated by extensive simulations. Finally, the statistical methodology has been applied to analyze the maize data mentioned before.     

Data reconciliation of nonnormal observations with nonlinear constraints

This paper presents a new method for the reconciliation of data described by arbitrary continuous probability distributions, with the focus on nonlinear constraints. The main idea, already applied to linear constraints in a previous paper, is to restrict the joint prior probability distribution of the observed variables with model constraints to get a joint posterior probability distribution. Because in general the posterior probability density function cannot be calculated analytically, it is shown that it has decisive advantages to sample from the posterior distribution by a Markov chain Monte Carlo (MCMC) method. From the resulting sample of observed and unobserved variables various characteristics of the posterior distribution can be estimated, such as the mean, the full covariance matrix, marginal posterior densities, as well as marginal moments, quantiles, and HPD intervals. The procedure is illustrated by examples from material flow analysis and chemical engineering.     

Adaptive LASSO for linear mixed model selection via profile log-likelihood

Mixed model selection is quite important in statistical literature. To assist the mixed model selection, we employ the adaptive LASSO penalized term to propose a two-stage selection procedure for the purpose of choosing both the random and fixed effects. In the first stage, we utilize the penalized restricted profile log-likelihood to choose the random effects; in the second stage, after the random effects are determined, we apply the penalized profile log-likelihood to select the fixed effects. In each stage, the Newton–Raphson algorithm is performed to complete the parameter estimation. We prove that the proposed procedure is consistent and possesses the oracle properties. The simulations and a real data application are conducted for demonstrating the effectiveness of the proposed selection procedure.