Optimal two-level conjoint designs with constant attributes in the profile sets

We propose a simple strategy to construct D-, A-, G- and V-optimal two-level designs for rating-based conjoint studies with large numbers of attributes. In order to simplify the rating task, the designs hold one or more attributes at a constant level in each profile set. Our approach combines orthogonal designs and binary incomplete block designs with equal replication. The designs are variance-balanced meaning that they yield an equal amount of information on each of the part-worths.     

从“小产权房”现象看我国住房保障出路

目前,我国大中城市房价昂贵,针对中低收入阶层的保障住房严重不足。顺应市场需要而产生的农村“小产权房”房价低廉,又有便利的交通与大中城市相连,因而能进入房产市场并迅速发展。“小产权房”虽有其不合法之处,但也预示着我国城市化发展过程中大中城市逆城市化时代的提前到来。统筹城乡规划,效仿新加坡建立科学合理的宏观、中观和微观的各级城镇乃至中心村规划,建立城乡统一的住房管理体系和住房保障,既能消除小产权房存在的基础,又是解决我国住房保障问题的合理出路。     

New 3-level response surface designs constructed from incomplete block designs

Box and Behnken [1958. Some new three level second-order designs for surface fitting. Statistical Technical Research Group Technical Report No. 26. Princeton University, Princeton, NJ; 1960. Some new three level designs for the study of quantitative variables. Technometrics 2, 455–475.] introduced a class of 3-level second-order designs for fitting the second-order response surface model. These 17 Box–Behnken designs (BB designs) are available for 3–12 and 16 factors. Although BB designs were developed nearly 50 years ago, they and the central-composite designs of Box and Wilson [1951. On the experimental attainment of optimum conditions. J. Royal Statist. Soc., Ser. B 13, 1–45.] are still the most often recommended response surface designs. Of the 17 aforementioned BB designs, 10 were constructed from balanced incomplete block designs (BIBDs) and seven were constructed from partially BIBDs (PBIBDs). In this paper we show that these seven BB designs constructed from PBIBDs can be improved in terms of rotatability as well as average prediction variance, D$D$- and G$G$-efficiency. In addition, we also report new orthogonally blocked solutions for 5, 8, 9, 11 and 13 factors. Note that an 11-factor BB design is available but cannot be orthogonally blocked. All new designs can be found at http://www.math.montana.edu/∼$\sim$jobo/bbd/.     

供应链中企业基于产品最终需求的博弈分析

供应链中零部件供应商在完全信息情况下的价格博弈模型表明:企业产品价格与自身的单位生产成本成正向变动关系,与对方企业的单位生产成本成反向变动关系。而不完全信息情况下的价格博弈模型表明:企业产品价格不但与各自的单位产品生产成本有关,还与下游企业对上游企业的期望单位产品生产成本也有关。     

基于变更的最优承包合同的研究

建设项目承包合同的不完全性、信息的非对称性以及承发包双方的信用危机共同作用，产生了隐藏信息的道德风险以及由此引起的非效率性问题、本研究采用动态博弈理论，建立了以政府机构为主导地位的，承发包双方针对施工条件变化，围绕着工期、合同价变更的不完全合同模型．研究表明，通过确定合理的施工条件、工期、承包价及合同变更规则，承包合同可以引导承发包双方投资，避免隐藏信息的道德风险，实现社会福利最优、     

TWO-WAY CHANGE-POINT MODEL AND ITS APPLICATION

Exact null and alternative distributions of the two-way maximally selected x² for interaction between the ordered rows and columns are derived for each of the normal and Poisson models, respectively. The method is one of the multiple comparison procedures for ordered parameters and is useful for defining a block interaction or a two-way change-point model as a simple alternative to the two-way additive model. The construction of a confidence region for the two-way change-point is then described. An important application is found in a dose-response clinical trial with ordered categorical responses, where detecting the dose level which gives significantly higher responses than the lower doses can be formulated as a problem of detecting a change in the interaction effects.     

Contingency tables with prescribed marginals

For an adjustment of contingency tables to prescribed marginal frequencies Deming and Stephan (1940) minimize a Chi-square expression. Asymptotically equivalently, Ireland and Kullback (1968) minimize a Leibler-Kullback divergence, where the probabilistical arguments for both methods remain vague. Here we deduce a probabilistical model based on observed contingency tables. It shows that the two above methods and the maximum likelihood approach in Smith (1947) yield asymptotically the ‘most probable’ adjustment under prescribed marginal frequencies. The fundamental hypothesis of statistical mechanics relates observations to ‘most probable’ realizations. ‘Most probable’ is going to be used in the sense of so-called large deviations. The proposed adjustment has a significant product form and will be generalized to contingency tables with infinitely many cells.     

Assigned Shares in Compensation for Radiation-Related Cancers

At the request of Congress, a Working Group of the National Institutes of Health prepared radioepidemiologic tables which estimate the likelihood that cancer victims previously exposed to a dose of radiation developed their cancer as a result of this exposure. The ultimate purpose of the tables is to provide a scientific basis for determining compensation for such victims, and their use would represent a marked departure from the current tort system for deciding compensation. The preparation of radioepidemiologic tables requires extensive mathematical modeling because matters such as sex, size of dose, age at exposure, type of cancer, and age at diagnosis must be taken into account. The limited data require many assumptions about the quantitative relationship between radiation dose and the age-specific incidence rate of cancer. After partitioning a population into reference sets based on age at exposure, size of dose, type of cancer, etc., an assigned share is computed for each reference set and then assigned to all of its members. The assigned share represents the fraction of the cancer cases in the reference set that are attributed to the radiation dose. Because the population can be partitioned in many ways, each individual's assigned share depends on the partition used and will change with different partitions. Options for modeling and limitations in epidemiologic data lead to considerable uncertainties in estimates of assigned shares that have been scientifically evaluated for the Working Group's tables. In contrast, the uncertainties associated with the current approach for determining the likelihood that a claimant's cancer was caused by radiation have not been appraised, but are likely to be even greater than those associated with the Working Group's tables. One issue is how to use such tables to compensate victims. Some among many possibilities are: to use them together with a compensation formula to determine the fraction of a standard award to be given; to use them as a starting value for the fraction, to be modified by an authority on the basis of additional information supplied by the claimant and defendant; and to use them as input to the present compensation system.     

不完备金融资产市场中的资本资产定价原理

本文中,我们在不完备金融资产市场的框架下研究了资本资产的定价问题,得到了著名的资本资产定价模型(CAPM)的一个重要推广形式,建立了相应的混合投资基金定理,这些结果对于金融资产市场的理论研究具有重要的意义。     

On the Analysis of Quasi-Life Tables

Baxter (1994) defined a quasi-life table in which the data arise from many concurrent, independent, discrete-time renewal processes. The processes are not observed individually, only the total numbers of renewals at each time point are observed. The estimates proposed by Baxter (1994), based on the discrete-time renewal equation, are studied more formally here, and some extensions are made.