Projection‐Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments

It is well known that standard asymptotic theory is not applicable or is very unreliable in models with identification problems or weak instruments. One possible way out consists of using a variant of the Anderson–Rubin ((1949), AR) procedure. The latter allows one to build exact tests and confidence sets only for the full vector of the coefficients of the endogenous explanatory variables in a structural equation, but not for individual coefficients. This problem may in principle be overcome by using projection methods (Dufour (1997), Dufour and Jasiak (2001)). At first sight, however, this technique requires the application of costly numerical algorithms. In this paper, we give a general necessary and sufficient condition that allows one to check whether an AR‐type confidence set is bounded. Furthermore, we provide an analytic solution to the problem of building projection‐based confidence sets from AR‐type confidence sets. The latter involves the geometric properties of “quadrics” and can be viewed as an extension of usual confidence intervals and ellipsoids. Only least squares techniques are needed to build the confidence intervals.     

高等教育最优投资双层规划模型研究

高等教育投资具有"双层"的特点,上层为省级主管部门,下层为高等学校。本文成功运用了双层规划模型,在不考虑高校自筹发展资金投入的情况下,建立了高等教育最优投资双层规划模型,研究了模型最优解的存在性,给出并证明了模型最优解的等价形式,设计了模型解的算法并进行了算法复杂性分析。通过求解模型,可以同时得到省级主管部门和高等学校的最优投资决策方案。文章最后还给出了考虑高校自筹发展资金的两种情况下建立投资模型和求得最优解的方法。     

技术创新对企业集团能量效率的影响与对策

引用动物捕食的最优方法的进化论观点研究了技术创新对企业集团能量效率的影响 ,提出了相应的对策 .首先 ,描述了一类企业集团的能量效率的基本模型 ,给出了一个关于技术与市场需求关系的假设 .接着 ,研究了技术创新对横向型企业集团能量效率的影响 ,在建立起模型之后 ,证明了提高核心企业的能量效率的充分性定理 ,为核心企业提供了对策方法 .然后 ,研究了核心企业是下游企业的纵向型企业集团 ,建立了模型 ,并获得了类似的结论 .最后 ,举例说明了核心企业应该怎样根据能量效率进行决策的思想 .总之 ,把一个企业集团的成长看成一群动物的进化 ,并且试图将进化论的思想应用到经济研究中     

Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression

We propose a novel statistic for conducting joint tests on all the structural parameters in instrumental variables regression. The statistic is straightforward to compute and equals a quadratic form of the score of the concentrated log–likelihood. It therefore attains its minimal value equal to zero at the maximum likelihood estimator. The statistic has a χ² limiting distribution with a degrees of freedom parameter equal to the number of structural parameters. The limiting distribution does not depend on nuisance parameters. The statistic overcomes the deficiencies of the Anderson–Rubin statistic, whose limiting distribution has a degrees of freedom parameter equal to the number of instruments, and the likelihood based, Wald, likelihood ratio, and Lagrange multiplier statistics, whose limiting distributions depend on nuisance parameters. Size and power comparisons reveal that the statistic is a (asymptotic) size–corrected likelihood ratio statistic. We apply the statistic to the Angrist–Krueger (1991) data and find similar results as in Staiger and Stock (1997).     

一类两层规划问题模糊满意解的遗传算法

在现有两层规划问题求解方法的基础上,提出用浮点数编码的遗传算法求解该问题模糊满意解的新方法．这种方法每次提供给决策者一组近似最优解,通过决策者的比较、评价和选择,在交互过程中得到各决策者都满意的解．该方法不仅可以给决策者提供更多的决策环境信息,而且可以适应决策者偏好的变化,使得决策过程更合理,更符合人的认识过程．     

带有交易费用的证券投资最优策略

在假设证券价格服从几何布朗运动的基础上,运用随机最优控制理论,研究了在ｎ 个风险证券金融市场中带有交易费用的证券投资问题,建立了带有交易费用的证券投资最优控制问题的数学模型．首先,简述了文中所涉及的随机最优控制理论,给出了值函数、效用函数和粘性解的定义．然后,在粘性解的意义下,推导出了交易策略有限和交易策略无限两种情况下值函数所满足的偏微分方程,该偏微分方程是由变分不等式描述的自由边值问题．最后,给出了两种情况下基于最优控制问题值函数的证券投资最优策略．本文得到的结果可以用于投资基金管理、金融风险管理等实际工作中,提高决策的科学性     

Fused least absolute shrinkage and selection operator for credit scoring

Credit scoring can be defined as the set of statistical models and techniques that help financial institutions in their credit decision makings. In this paper, we consider a coarse classification method based on fused least absolute shrinkage and selection operator (LASSO) penalization. By adopting fused LASSO, one can deal continuous as well as discrete variables in a unified framework. For computational efficiency, we develop a penalization path algorithm. Through numerical examples, we compare the performances of fused LASSO and LASSO with dummy variable coding.     

Assessing goodness-of-fit of categorical regression models based on case-control data

Demonstrated equivalence between a categorical regression model based on case‐control data and an I‐sample semiparametric selection bias model leads to a new goodness‐of‐fit test. The proposed test statistic is an extension of an existing Kolmogorov–Smirnov‐type statistic and is the weighted average of the absolute differences between two estimated distribution functions in each response category. The paper establishes an optimal property for the maximum semiparametric likelihood estimator of the parameters in the I‐sample semiparametric selection bias model. It also presents a bootstrap procedure, some simulation results and an analysis of two real datasets.     

关于Feigenbaum型泛函方程的C^1解

利用Schauder不动点定理、自同胚和紧凸子集的相关性质研究Feigenbaum型泛函方程的连续可微解的存在性和唯一性.