Mixture experiments with mixing errors

In mixture experiments the properties of mixtures are usually studied by mixing the amounts of the mixture components that are required to obtain the necessary proportions. This paper considers the impact of inaccuracies in discharging the required amounts of the mixture components on the statistical analysis of the data. It shows how the regression calibration approach can be used to minimize the resulting bias in the model and in the estimates of the model parameters, as well as to find correct estimates of the corresponding variances. Its application is made difficult by the complex structure of these errors. We also show how knowledge of the form of the model bias allows for choosing a manufacturing setting for a mixture product that is not biased and has smaller signal to noise ratio.     

正交多项式回归模型参数估计的格子设计及其最小二乘估计

对二元二次多项式回归模型进行预先正交化处理，提出使用因子空间的N等份的格子设计的观点，推导出了信息矩阵的一般性结构，并给出了该设计的非退化条件及其最小二乘估计和对应的协方差矩阵。     

"三三制"政权:中国共产党民主执政的实验场

"三三制"政权是中国共产党在抗日战争时期所创建和领导的民主政权形式,"三三制"政权建设的实践,实际上是中国共产党民主执政的一次重要实验,为中国共产党今天的民主执政积累了历史经验和借鉴意义.     

珠三角的“自梳女”

“自梳女”是珠江三角洲特有的一种婚嫁习俗 ,兴起于明代 ,盛行于清代 ,是当时妇女对封建婚姻制度的一种畸形的反抗。其形式有三 :义结金兰、独身终老和不落家。这与珠三角资本主义经济萌芽 ,丝织业迅速发展有关。它与西方的同性恋不同 ,但与现代妇女的非婚现象却有点相似。今日珠三角女工大批云集 ,历史的经验值得注意。     

弱连续格及其性质

给出了弱连续格的概念 ,讨论了弱连续格的若干重要性质 ,用分配性刻划了弱连续格     

Al_（0．3）Ga_（0．7）As／GaAs超晶格在高能高温注入下的晶格损伤

用卢瑟福背散射／沟道技术研究了ＩＭｅＶＳｉ￣＋衬底加温注入Ａｌ_（０．３）Ｇａ_（０．７）Ａｓ／ＧａＡｓ超晶格和作为比较的ＧａＡｓ晶体后晶格的损伤积累与注入剂量的关系。实验结果表明，在注入剂量比较小的情况下，两种晶体都只有很轻微的损伤；动态退火过程的存在抑制了晶格损伤的积累。但在较高的注入剂量下，在几乎无损伤的表面下两种晶体中都形成了损伤埋层，且ＧａＡｓ中损伤峰处的损伤程度和损伤峰的宽度都大于Ａｌ_（０．３）Ｇａ_（０．７）Ａｓ／ＧａＡｓ超晶格中的情形，根据级联碰撞理论分析了晶体中的损伤积累过程，并从化学键相对强度差异的角度定性地解释了ＧａＡｓ和Ａｌ_（０．３）Ｇａ_（０．７）Ａｓ／ＧａＡｓ超晶格实验结果的不同。     

Choice of alpha spending function and time points in clinical trials with one or two interim analyses

One characterization of group sequential methods uses alpha spending functions to allocate the false positive rate throughout a study. We consider and evaluate several such spending functions as well as the time points of the interim analyses at which they apply. In addition, we evaluate the double triangular test as an alternative procedure that allows for early termination of the trial not only due to efficacy differences between treatments, but also due to lack of such differences. We motivate and illustrate our work by reference to the analysis of survival data from a proposed oncology study. Such group sequential procedures with one or two interim analyses are only slightly less powerful than fixed sample trials, but provide for the strong possibility of early stopping. Therefore, in all situations where they can practically be applied, we recommend their routine use in clinical trials. The double triangular test provides a suitable alternative to the group sequential procedures in that they do not provide for early stopping with acceptance of the null hypothesis. Again, there is only a modest loss in power relative to fixed sample tests. Copyright © 2004 John Wiley & Sons, Ltd.     

The double triangular test in practice

The double triangular test was introduced twenty years ago, and the purpose of this paper is to review applications that have been made since then. In fact, take‐up of the method was rather slow until the late 1990s, but in recent years several clinical trial reports have been published describing its use in a wide range of therapeutic areas. The core of this paper is a detailed account of five trials that have been published since 2000 in which the method was applied to studies of pancreatic cancer, breast cancer, myocardial infarction, epilepsy and bedsores. Before those accounts are given, the method is described and the history behind its evolution is presented. The future potential of the method for sequential case–control and equivalence trials is also discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

Competition and evolutionary stability of plants in a spatially structured habitat

We modelled the population dynamics of two types of plants with limited dispersal living in a lattice structured habitat. Each site of the square lattice model was either occupied by an individual or vacant. Each individual reproduced to its neighbors. We derived a criterion for the invasion of a rare type into a population composed of a resident type based on a pair-approximation method, in which the dynamics of both average densities and the nearest neighbor correlations were considered. Based on this invasibility criterion, we showed that, when there is a tradeoff between birth and death rates, the evolutionarily stable type is the one that has the highest ratio of birth rate to mortality. If these types are different species, they form segregated spatial patterns in the lattice model in which intraspecific competitive interactions occur more frequently than interspecific interactions. However, stable coexistence is not possible in the lattice model contrary to results from completely mixed population models. This clearly shows that the casual conclusion, based on traditional well mixed population models, that different species can coexist if intraspecific competition is stronger than interspecific competition, does not hold for spatially structured population models.     

Quasi-random resampling for the bootstrap

Quasi-random sequences are known to give efficient numerical integration rules in many Bayesian statistical problems where the posterior distribution can be transformed into periodic functions on then-dimensional hypercube. From this idea we develop a quasi-random approach to the generation of resamples used for Monte Carlo approximations to bootstrap estimates of bias, variance and distribution functions. We demonstrate a major difference between quasi-random bootstrap resamples, which are generated by deterministic algorithms and have no true randomness, and the usual pseudo-random bootstrap resamples generated by the classical bootstrap approach. Various quasi-random approaches are considered and are shown via a simulation study to result in approximants that are competitive in terms of efficiency when compared with other bootstrap Monte Carlo procedures such as balanced and antithetic resampling.