Bayesian D-optimal Accelerated Life Test plans for series systems with competing exponential causes of failure

This paper provides methods of obtaining Bayesian D-optimal Accelerated Life Test (ALT) plans for series systems with independent exponential component lives under the Type-I censoring scheme. Two different Bayesian D-optimality design criteria are considered. For both the criteria, first optimal designs for a given number of experimental points are found by solving a finite-dimensional constrained optimization problem. Next, the global optimality of such an ALT plan is ensured by applying the General Equivalence Theorem. A detailed sensitivity analysis is also carried out to investigate the effect of different planning inputs on the resulting optimal ALT plans. Furthermore, these Bayesian optimal plans are also compared with the corresponding (frequentist) locally D-optimal ALT plans.     

Treatment allocation strategies for umbrella trials in the presence of multiple biomarkers: A comparison of methods

Umbrella trials are an innovative trial design where different treatments are matched with subtypes of a disease, with the matching typically based on a set of biomarkers. Consequently, when patients can be positive for more than one biomarker, they may be eligible for multiple treatment arms. In practice, different approaches could be applied to allocate patients who are positive for multiple biomarkers to treatments. However, to date there has been little exploration of how these approaches compare statistically. We conduct a simulation study to compare five approaches to handling treatment allocation in the presence of multiple biomarkers – equal randomisation; randomisation with fixed probability of allocation to control; Bayesian adaptive randomisation (BAR); constrained randomisation; and hierarchy of biomarkers. We evaluate these approaches under different scenarios in the context of a hypothetical phase II biomarker-guided umbrella trial. We define the pairings representing the pre-trial expectations on efficacy as linked pairs, and the other biomarker-treatment pairings as unlinked. The hierarchy and BAR approaches have the highest power to detect a treatment-biomarker linked interaction. However, the hierarchy procedure performs poorly if the pre-specified treatment-biomarker pairings are incorrect. The BAR method allocates a higher proportion of patients who are positive for multiple biomarkers to promising treatments when an unlinked interaction is present. In most scenarios, the constrained randomisation approach best balances allocation to all treatment arms. Pre-specification of an approach to deal with treatment allocation in the presence of multiple biomarkers is important, especially when overlapping subgroups are likely.     

Mixture designs for product improvement studies

Many products are mixtures of several components (ingredient). Characteristics of the products such as the strength of steel, the efficacy of a chemical pesticide, or the viscosity of a liquid detergent, depend only on the relative proportions of the components in the mixture. Studying changes in a product' properties caused by varying the ingredient proportions is the objective of performing mixture experiments. The inherent restriction that the sum of the component proportions equal unity creates different design strategies than are usually employed with independent factors where factorial arrangements are quite common. Experimental designs for exploring the entire mixture simplex region as well as for exploring only a subregion of the simplex are presented. In those cases where four or more components are considered and a subregion is to be investigated, computer-aided designs are the rule rather than the exception. Design criterion based on the properties (variance and bias) of the prediction equation are mentioned briefly and some suggestions are made for future research in mixture experiments.     

Mean square error and efficiency of the least squares estimator over interval constraints

We derive the mean square error of an interval constrained least squares estimator (INCLS) for a regression model. We then show that the INCLS estimator dominates, in mean square error, the unconstrained least squares estimator provided the regression residuais are normally distri'iiuted and Ynat Yrie imposed coii-

straint is satisfied or nearly satisfied.     

A closed form solution for tre least squares regression problem with linear inequality constraints

In this paper we consider a linear model Y = Xβ+e with linear inequality constraints R'β≥r, where X and R are known and full column rank matrices. The closed form of the inequality constrained least squares (ICLS) estimator is given. We provide two examples which illustrate the use of this closed form in the computation of estimates.     

Estimation and hypothesis in linear models-A reparameterization approach to the cell mlans modll

A general approach to analysis of fixed effects models through a reparameterization of the cell means model is outlined. After applying a Q-op3rator, distribution theory for the model is developed. Methods of estimation and hypothesis testing are given and the exact form of each hypothesis is shown. The implementation of these results in a currently available computer package is discussed.     

Telecommunications Network Design—Comparison of Alternative Approaches

The design and development of the network infrastructure to support mission‐critical applications has become a critical and‐complex activity. This study explores the use of genetic algorithms (GA) for network design in the context of degree‐constrained minimal spanning tree (DCMST) problem; compares for small networks the performance of GA with a mathematical model that provides optimal solutions; and for larger networks, compares GA's performance with two heuristic methods—edge exchange and primal algorithm. Two performance measures, solution quality and computation time, are used for evaluation. The algorithms are evaluated on a wide variety of network sizes with both static and dynamic degree constraints on the network nodes. The results indicate that GA provides optimal solutions for small networks. For larger networks it provides better solution quality compared to edge exchange and primal method, but is worse than the two methods in computation time.     

中国股票市场行业与地区效应分析

根据国家行业分类,参照地区的远近和经济发达程度,把中国股票市场的股票划分为21个行业、12个地区。依据中国股票市场从1995年7月到2001年6月的股票回报率月数据,利用约束回归分析法对回报率的行业和地区效应进行了横截面和时间序列分析,表明中国股票市场具有明显的行业和地区效应,并且行业效应大于地区效应。     

AN EXCLUSIVE REGRESSORS BINARY MIXTURE MODEL WITH AN APPLICATION TO LABOUR SUPPLY

This paper suggests a new type of mixture regression model, in which each mixture component is explained by its own regressors. Thus, the dependent variable can be driven by one of several unobservable explanatory mechanisms, each of which has its own distinct variables. An extension of the simulated annealing algorithm is introduced to fit this general mixture model. The paper also suggests a new technique for estimating the covariance matrix of estimators in a mixture model. Finally, empirical studies of a labour supply example show that our proposed model can perform much better than conventional logistic or mixture models.     

MVDR波束形成最佳权矢量的直接提取

描述一种用于计算最小方差无失真响应准则(MVDR)波束形成最佳权矢量的三角形Systolic阵列。提出了一种称为“权冲洗”的新方法,不需要增加任何线性Systolic阵列,便能直接从三角形Systolic阵列中提取最佳权矢量。该方法非常简单、容易实现。