Optimal Prediction in Stochastic Regression Models with Application to the Analysis of Repeated Surveys

Several results relating to the optimal prediction of regression coefficients and random variables under a general linear model with stochastic coefficients are presented. These results are then applied to the analysis of repeated sample surveys over time. In particular, if the finite population can be modelled by a superpopulation model, a fully efficient method for the analysis of repeated surveys is proposed.     

On the distribution of quadratic forms in normal random variables

This paper provides necessary and sufficient conditions for a quadratic form in singular normal random variables to be distributed as a given linear combination of independent noncentral chi-square variables. Using this result, an extension of Cochran's theorem to quadratic forms of noncentral chi-square variables is derived.     

Length-Biassed Sampling from a Finite Population

Expressions are derived for the interval moments of a length-biassed sample from a renewal process of finite length.     

用算子展开法求解 Fredholm 积分方程

提供了另一种求解积分方程的方法。利用 Hilbert 空间来研究 Fredholm 积分算子,并证明了可利用一组标准正交基将 Fredholn 积分算子展开,从而使积分方程得到简化。应用这一方法给出了一般第二类 Fredholm 积分方程的严格解析解。文中还对具体积分方程进行了求解并与严格解和其它方法所得的解进行了比较,结果吻合得很好。     

Recursive Equilibrium in Stochastic Overlapping‐Generations Economies

We prove the generic existence of a recursive equilibrium for overlapping‐generations economies with uncertainty. “Generic” here means in a residual set of utilities and endowments. The result holds provided there is a sufficient number of potentially different individuals within each cohort.     

一个政府行为的组织学分析——以广州市恩宁路旧城改造为例

以政府主导的旧城改造运动频频上演,背后的利益冲突日益突出。分析其原因发现,在微观层面上,是因为组织设计中的激励机制如晋升机制、考核机制、上下级之间的信息不对称等诱发了政府官员有着追求政绩工程的强烈动机;在宏观层面上,是因为组织制度对城市基层政府的旧城改造行为缺乏有效约束,来自社会的力量未对基层政府的行为产生有效的影响。微观和宏观层面的双重原因,致使城市政府热衷于旧城改造,并且在不同的地区、不同的城市反复出现。     

四色定理的简洁证明及其意义

严格分析四色定理成立的条件,即可以用简洁方法证明四色定理。这一证明对于认识论和思维科学研究有重要意义。     

三阶中立型分布时滞阻尼微分方程的振动定理

研究一类三阶非线性中立型阻尼泛函微分方程,利用Riccati变换和积分平均技巧,建立了保证该类方程的一切解振动或者收敛于零的若干新的充分条件,推广和改进最近文献的结果.     

Statistical Properties of Model-Based Signal Extraction Diagnostic Tests

The problem of choosing the loss function in the Bayesian problem of many hypotheses testing is considered. It is shown that linear and quadratic loss functions are the most-used ones. For any kind of loss function, the risk function in the Bayesian problem of many hypotheses testing contains the errors of two kinds. The Bayesian decision rule minimizes the total effect of these errors. The share of each of them in the optimal value of risk function is unknown. When solving many important problems, the results caused by different errors significantly differ from each other. Therefore, it is necessary to guarantee the limitation on the most undesirable kind of these errors and to minimize the errors of the second kind. For solving these problems, this article are states and solves conditional Bayesian tasks of testing many hypotheses. The results of sensitivity analysis of the classical and conditional Bayesian problems are given and their advantages and drawbacks are considered.     

A New Goodness-of-Fit Test Based on the Empirical Characteristic Function

In this article, we present a goodness-of-fit test for a distribution based on some comparisons between the empirical characteristic function c_n(t) and the characteristic function of a random variable under the simple null hypothesis, c₀(t). We do this by introducing a suitable distance measure. Empirical critical values for the new test statistic for testing normality are computed. In addition, the new test is compared via simulation to other omnibus tests for normality and it is shown that this new test is more powerful than others.