Group up-and-down designs for dose-finding

Let toxicity to treatment be a Bernoulli random variable for which the probability of failure increases with dose. Consider the problem of identifying a dose $\mu$ having pre-specified probability of failure using data from groups of subjects who arrive sequentially for treatment. There is considerable theory available in this setting for fully sequential up-and-down procedures. This paper presents asymptotic and finite theoretical results for Markovian up-and-down procedures when subjects are treated in groups. Practical instructions are given on how to select the design parameters so as to cause the treatments to cluster around the unknown dose $\mu$. Examples are given to illustrate how this group procedure behaves for small sample sizes.     

Exact Confidence Intervals for Proportions Estimated by Group Testing with Different Group Sizes

Group testing is the process of combining individual samples and testing them as a group for the presence of an attribute. The use of such testing to estimate proportions is an important statistical tool in many applications. When samples are collected and tested in groups of different size, complications arise in the construction of exact confidence intervals. In this case, the numbers of positive groups has a multivariate distribution, and the difficulty stems from a lack of a natural ordering of the sample points. Exact two‐sided intervals such as the equal‐tail method based on maximum likelihood estimation, and those based on joint probability or likelihood ratio statistics, have been previously considered. In this paper several new estimators are developed and assessed. We show that the combined tails (or Blaker) method based on a suitable ordering statistic, is the best choice in this setting. The methods are illustrated using a study involving the infection prevalence of Myxobolus cerebralis among free‐ranging fish.     

Optimal Binary Prediction for Group Decision Making

We address the problem of optimally forecasting a binary variable for a heterogeneous group of decision makers facing various (binary) decision problems that are tied together only by the unknown outcome. A typical example is a weather forecaster who needs to estimate the probability of rain tomorrow and then report it to the public. Given a conditional probability model for the outcome of interest (e.g., logit or probit), we introduce the idea of maximum welfare estimation and derive conditions under which traditional estimators, such as maximum likelihood or (nonlinear) least squares, are asymptotically socially optimal even when the underlying model is misspecified.     

Group variable selection for data with dependent structures

Variable selection methods have been widely used in the analysis of high-dimensional data, for example, gene expression microarray data and single nucleotide polymorphism data. A special feature of the genomic data is that genes participating in a common metabolic pathway or sharing a similar biological function tend to have high correlations. The collinearity naturally embedded in these data requires special handling, which cannot be provided by existing variable selection methods. In this paper, we propose a set of new methods to select variables in correlated data. The new methods follow the forward selection procedure of least angle regression (LARS) but conduct grouping and selecting at the same time. The methods specially work when no prior information on group structures of data is available. Simulations and real examples show that our proposed methods often outperform the existing variable selection methods, including LARS and elastic net, in terms of both reducing prediction error and preserving sparsity of representation.     

Group selection for processes with multiple quality characteristics

Evaluating and comparing process capabilities are important tasks of production management. Manufacturers should apply the process with the highest capability among competing processes. A process group selection method is developed to solve the process selection problem based on overall yields. The goal is to select the processes with the highest overall yield among I processes under multiple quality characteristics, I > 2. The proposed method uses Bonferroni adjustment to control the overall error rate of comparing multiple processes. The critical values and the required sample sizes for designated powers are provided for practical use.     

Group and within-group variable selection for competing risks data

Variable selection in the presence of grouped variables is troublesome for competing risks data: while some recent methods deal with group selection only, simultaneous selection of both groups and within-group variables remains largely unexplored. In this context, we propose an adaptive group bridge method, enabling simultaneous selection both within and between groups, for competing risks data. The adaptive group bridge is applicable to independent and clustered data. It also allows the number of variables to diverge as the sample size increases. We show that our new method possesses excellent asymptotic properties, including variable selection consistency at group and within-group levels. We also show superior performance in simulated and real data sets over several competing approaches, including group bridge, adaptive group lasso, and AIC / BIC-based methods.     

A Multivariate Group Runs Control Chart for Process Dispersion

In this article, control charts for bivariate as well as for multivariate normal data are proposed to detect a shift in the process variability. Methods of obtaining design parameters and procedures of implementing the proposed charts are discussed. Performance of the proposed charts is compared with some existing control charts. It is verified that the proposed charts significantly reduce the out of control “average run length” (ARL) as compared to other charts considered in the study. Also, when the process variability decreases (process improvement), it is verified that the ARL of the proposed multivariate control chart increases as compared to other charts considered in the study.     

Group selection for production yield among k manufacturing lines

Producing qualified items or products is essential to meet the requirement preset by customers. Evaluation and selection of desired manufacturing lines become challenging tasks for decision makers. Production yield is one of the important factors in measuring production performance. The goal of this paper is to screen a group of manufacturing lines and identify the best one with the highest yield. For the production lines with extremely low fraction of defectives, the yield index, S_pk, is an efficient indicator for quality level. This paper considers the production selection problem by using S_pk to compare k (k>2) manufacturing lines. A subset is constructed to contain the production lines with the highest yield. A systematic approach of test order k compares selected pairs of manufacturing lines along with the Bonferroni method is proposed to solve this problem. Each pair of production yields is compared by taking ratio. The paper provides critical values and required sample sizes of the group selection procedure. An application example on evaluating four power inductor productions is presented to illustrate the practicality of the proposed approach.     

Catalogue of Group Structures for Three-level Fractional Factorial Designs

Taguchi (1959) introduced the concept of split-unit design to sort the factors into different groups depending upon the difficulties involved in changing the levels of factors. Li et al. (1991) renamed it as split-plot design. Chen et al. (1993) have given a catalogue of small designs for two- and three-level fractional factorial designs pertaining to a single type of factors. Aggarwal et al. (1997) have given a catalogue of group structure for two-level fractional factorial designs developed under the concept of split-plot design. In this paper, an algorithm has been developed for generating group structure and possible allocations for various 3^n-k fractional factorial designs.     

GSIS超高维变量选择

变量选择在超高维统计模型中非常重要。Fan和Lv基于简单相关系数提出确保独立筛选法(SIS),但当自变量被分成组时,SIS就会失效。因为SIS只能对单个变量进行选择,不能对组变量进行选择。为此,基于边际组回归提出组确保独立筛选法(GSIS),该方法不仅对组变量有效,对单个变量也有效,或者两者的混合也同样有效。Monte Carlo模拟结果显示,GSIS的表现优于SIS。     

第四届全国统计教材编审委员会第二次全体会议小组讨论纪要综述

第四届全国统计教材编审委员会(以下简称:编委会)第二次全体会议于2 0 0 3年12月在海口市召开。会议的一项重要议题是讨论统计教材建设和统计教学改革。来自全国各有关高等院校的5 0多名代表分别就统计学、数理统计、多元统计分析、国民经济统计和经济计量学等课程的教材建设和     

Development of Adaptive Group Sequential Procedure for Changing Sample Size

In this study, we propose a group sequential procedure that allows the change of necessary sample size at intermediary stage in sequential test. In the procedure, we formulate the conditional power to judge the necessity of the change of sample size in decision rules. Furthermore, we present an integral formula of the power of the test and show how to change the necessary sample size by using the power of the test. In simulation studies, we investigate the characteristics of the change of sample size and the pattern of decision across all stages based on generated normal random numbers.     

A New Estimator for a Population Proportion Using Group Testing

The maximum likelihood estimator is widely used in estimating the population proportion using group testing. However, it is positive biased and some alternatives have been raised in literatures. In this study, we propose a new estimator by weighted combination of order statistics. Two rules are supplied to determine the unknown weight. Using the rule of minimizing the absolute bias, our estimator is almost unbiased in most cases shown by simulations. Using the rule of minimizing the mean square error, a simple estimator with weight 1 is recommended for its good performance.