On empirical likelihood for semiparametric two-sample density ratio models

We consider estimation and test problems for some semiparametric two-sample density ratio models. The profile empirical likelihood (EL) poses an irregularity problem under the null hypothesis that the laws of the two samples are equal. We show that a dual form of the profile EL is well defined even under the null hypothesis. A statistical test, based on the dual form of the EL ratio statistic (ELRS), is then proposed. We give an interpretation for the dual form of the ELRS through φ$\phi$-divergences and duality techniques. The asymptotic properties of the test statistic are presented both under the null and the alternative hypotheses, and approximation of the power function of the test is deduced.     

卖方边际成本可变的多物品多属性逆向拍卖研究

研究卖方边际成本可变的多物品多属性逆向拍卖问题。首先,根据卖方边际成本可变的特点设计了一种多轮逆向拍卖机制;其次,基于近视最佳反应策略的基本假设,分析卖方的投标策略;最后,利用仿真实验方法,研究买方事先公布估价信息对拍卖的影响。基本结果是:本拍卖机制在多数情况下是有效率的;相对买方不公布估价信息的拍卖机制,买方事先公布估价信息的多物品多属性拍卖具有稍差的市场效率,但能够显著地提高拍卖收敛速度。     

Conditional quantile estimation with auxiliary information for left-truncated and dependent data

In this paper, the empirical likelihood method is used to define a new estimator of conditional quantile in the presence of auxiliary information for the left-truncation model. The asymptotic normality of the estimator is established when the data exhibit some kind of dependence. It is assumed that the lifetime observations with multivariate covariates form a stationary α‐mixing sequence. The result shows that the asymptotic variance of the proposed estimator is not larger than that of standard kernel estimator. Finite sample behavior of the estimator is investigated via simulations too.     

Selecting and checking a binomial response generalized linear model using phi-divergences

This work introduces specific tools based on phi-divergences to select and check generalized linear models with binary data. A backward selection criterion that helps to reduce the number of explanatory variables is considered. Diagnostic methods based on divergence measures such as a new measure to detect leverage points and two indicators to detect influential points are introduced. As an illustration, the diagnostics are applied to human psychology data.     

Using pilot study information to increase efficiency in clinical trials

It is often necessary to conduct a pilot study to determine the sample size required for a clinical trial. Due to differences in sampling environments, the pilot data are usually discarded after sample size calculation. This paper tries to use the pilot information to modify the subsequent testing procedure when a two-sided t$t$-test or a regression model is used to compare two treatments. The new test maintains the required significance level regardless of the dissimilarity between the pilot and the target populations, but increases the power when the two are similar. The test is constructed based on the posterior distribution of the parameters given the pilot study information, but its properties are investigated from a frequentist's viewpoint. Due to the small likelihood of an irrelevant pilot population, the new approach is a viable alternative to the current practice.     

D-optimal designs for logistic models with three and four parameters

Logistic functions are used in different applications, including biological growth studies and assay data analysis. Locally D-optimal designs for logistic models with three and four parameters are investigated. It is shown that these designs are minimally supported. Efficiencies are computed for equally spaced and uniform designs.     

《九章》阐释三题

重新考查屈原的生平 ,《抽思》当作于屈原被放逐到汉北之初即楚怀王十八年 (前 3 11) ,是写来献给怀王表明心迹的 ;《涉江》作于顷襄王决定将屈原流放到溆浦山中之时 ,诗人的情绪特别悲愤 ,诗中表达了宁折不弯的性格和操守 ;《惜往日》作于自沉以前不久 ,其中总结楚国失败的教训 ,与大败楚师之秦将白起的有关分析合若符契。     

《老子》楚简本、帛书本、通行本比较研究

识 ,甲本德篇的圆点就是这种标志的残留。随着经过编辑的《老子》文本在社会上的广泛流传 ,篇章之间的聚合力不断加强 ,而标志符号的作用却不断减弱 ,直到最后完全取消 ,好象这些篇章本来就连在一起似的 ,这是一个合于逻辑的发展过程。帛甲本中标志符号的使用情况说明 ,当时社会上流传的《老子》正处于有标识文本向无标识文本的过渡阶段。帛乙抄录于帛甲之后 ,其间已没有任何标志符号 ,说明《老子》编辑成书的过程已经完成。书中原来存留的标志篇章编次组合的符号 ,也已完成其使命而不再抄录于文本当中。随着社会的发展 ,这种没有任何标志的…