Group sequential x2 statistic for testing the difference of two mean vectors in clinical trials

In this study we discuss the group sequential procedures for comparing two treatments based on multivariate observations in clinical trials. Also we suppose that a response vector on each of two treatments has a multivariate normal distribution with unknown covariance matrix. Then we propose a group sequential x² statistic in order to carry out repeated significance test for hypothesis of no difference between two population mean vectors. In order to realize the group sequential test where average sample number is reduced, we propose another modified group sequential x² statistic by extension of Jennison and Turnbull ( 1991 ). After construction of repeated confidence boundaries for making the repeated significance test, we compare two group sequential procedures based on two statistics regarding the average sample number and the power of the test in the simulations.     

Shrinkage inverse regression estimation for model-free variable selection

Summary.  The family of inverse regression estimators that was recently proposed by Cook and Ni has proven effective in dimension reduction by transforming the high dimensional predictor vector to its low dimensional projections. We propose a general shrinkage estimation strategy for the entire inverse regression estimation family that is capable of simultaneous dimension reduction and variable selection. We demonstrate that the new estimators achieve consistency in variable selection without requiring any traditional model, meanwhile retaining the root n estimation consistency of the dimension reduction basis. We also show the effectiveness of the new estimators through both simulation and real data analysis.     

Improving Risk Management: From Lame Excuses to Principled Practice

The three classic pillars of risk analysis are risk assessment (how big is the risk and how sure can we be?), risk management (what shall we do about it?), and risk communication (what shall we say about it, to whom, when, and how?). We propose two complements as important parts of these three bases: risk attribution (who or what addressable conditions actually caused an accident or loss?) and learning from experience about risk reduction (what works, and how well?). Failures in complex systems usually evoke blame, often with insufficient attention to root causes of failure, including some aspects of the situation, design decisions, or social norms and culture. Focusing on blame, however, can inhibit effective learning, instead eliciting excuses to deflect attention and perceived culpability. Productive understanding of what went wrong, and how to do better, thus requires moving past recrimination and excuses. This article identifies common blame‐shifting “lame excuses” for poor risk management. These generally contribute little to effective improvements and may leave real risks and preventable causes unaddressed. We propose principles from risk and decision sciences and organizational design to improve results. These start with organizational leadership. More specifically, they include: deliberate testing and learning—especially from near‐misses and accident precursors; careful causal analysis of accidents; risk quantification; candid expression of uncertainties about costs and benefits of risk‐reduction options; optimization of tradeoffs between gathering additional information and immediate action; promotion of safety culture; and mindful allocation of people, responsibilities, and resources to reduce risks. We propose that these principles provide sound foundations for improving successful risk management.     

Transition probabilities and ARL performance of Six Sigma zone control charts

In this article, Six Sigma zone control charts (SSZCCs) are proposed for world class organizations. The transition probabilities are obtained using the Markov chain approach. The Average Run Length (ARL) values are then presented. The ARL performance of the proposed SSZCCs and the standard Six Sigma control chart (SSCC) without zones or run rules is studied. The ARL performance of these charts is then compared with those of the other standard zone control charts (ZCCs), the modified ZCC and the traditional Shewhart control chart (SCC) with common run rules. As expected, it is shown that the proposed SSZCC outperforms the standard SSCC without zones or run rules for process shifts of any magnitude. When compared to the other standard ZCCs and the Shewhart chart with common run rules, it is observed that the proposed SSZCCs have much higher false alarm rates for smaller shifts and hence they prevent unwanted process disturbances. The application of the proposed SSZCC is illustrated using a real time example.     

浅析高中数学有效教学的内涵、特征及实施策略

高中数学有效教学的涵义即在数学课程标准基本理念的指导下，促进学生数学学习、提高学生数学素养、促成学生终身发展．高中数学有效教学的主要特征是教学目标有效、教学过程有效、教学方式有效、教学结果有效。主要实施策略是，以引导探究为依托，实现有效的知识建构；以暴露思维作平台，实现有效的思维训练；以激发兴趣作前提，实现有效的情意驱动．     

Functional Partial Linear Single‐index Model

This paper deals with the problem of predicting the real‐valued response variable using explanatory variables containing both multivariate random variable and random curve. The proposed functional partial linear single‐index model treats the multivariate random variable as linear part and the random curve as functional single‐index part, respectively. To estimate the non‐parametric link function, the functional single‐index and the parameters in the linear part, a two‐stage estimation procedure is proposed. Compared with existing semi‐parametric methods, the proposed approach requires no initial estimation and iteration. Asymptotical properties are established for both the parameters in the linear part and the functional single‐index. The convergence rate for the non‐parametric link function is also given. In addition, asymptotical normality of the error variance is obtained that facilitates the construction of confidence region and hypothesis testing for the unknown parameter. Numerical experiments including simulation studies and a real‐data analysis are conducted to evaluate the empirical performance of the proposed method.     

基于熵权法的江苏生态环境高质量发展评价研究

针对生态环境内涵的多样性,结合传统高质量发展的评价指标,从环境质量、排放强度、污染治理和资源利用4个维度构建生态环境高质量发展评价指标体系,并基于熵权法提出指标量化和评估数据预处理的解决方案。结果表明:2010—2019年江苏生态环境质量水平由“缓慢增长”向“波动下降”转变,污染治理和资源利用成为改善现阶段生态环境质量的重要突破口,政府、社会、企业、个人等主体可从循环经济、人居环境、水环境综合治理角度进行生态环境的整治。     

Bayesian inference for stable Lévy–driven stochastic differential equations with high‐frequency data

In this paper, we consider parametric Bayesian inference for stochastic differential equations driven by a pure‐jump stable Lévy process, which is observed at high frequency. In most cases of practical interest, the likelihood function is not available; hence, we use a quasi‐likelihood and place an associated prior on the unknown parameters. It is shown under regularity conditions that there is a Bernstein–von Mises theorem associated to the posterior. We then develop a Markov chain Monte Carlo algorithm for Bayesian inference, and assisted with theoretical results, we show how to scale Metropolis–Hastings proposals when the frequency of the data grows, in order to prevent the acceptance ratio from going to zero in the large data limit. Our algorithm is presented on numerical examples that help verify our theoretical findings.