A strong law of large numbers for independent random variables under non-additive probabilities

Abstract

Under non‐additive probabilities, cluster points of the empirical average have been proved to quasi-surely fall into the interval constructed by either the lower and upper expectations or the lower and upper Choquet expectations. In this paper, based on the initiated notion of independence, we obtain a different Marcinkiewicz-Zygmund type strong law of large numbers. Then the Kolmogorov type strong law of large numbers can be derived from it directly, stating that the closed interval between the lower and upper expectations is the smallest one that covers cluster points of the empirical average quasi-surely.     

全球价值链嵌入与技术创新——基于生产分解模型的分析

基于增加值和最终产品的生产分解模型,本文对我国制造业前向与后向产业关联下的全球价值链嵌入进行测度,实证分析全球价值链嵌入对技术创新的作用机理,并在此基础上重点探讨了吸收能力与技术差距两个重要情境因素的调节作用,同时,运用双重差分、工具变量法以及GMM动态面板模型进行稳健性检验,以控制潜在的内生性问题。研究发现:①我国制造业通过嵌入全球价值链的国际间知识溢出效应促进技术创新能力的提升;②吸收能力能够强化这一正向影响关系;③技术差距在后向全球价值链嵌入对技术创新的影响关系中呈倒U 型调节作用,而在前向全球价值链嵌入对技术创新的影响关系中呈正向调节作用。本文推动了网络嵌入理论和知识溢出理论从组织网络向全球价值链领域的繁衍,丰富了全球价值链嵌入领域的研究成果,同时为我国制造业企业在参与国际分工过程中利用全球价值链嵌入实现技术创新能力提升提供重要的理论参考。     

中国粮食增产的主要因素贡献分解与实证估算

已有测算中国粮食增产要素贡献率的方法存在虚增或低估某要素贡献率的缺陷,文章通过改进粮食增产贡献率测算方法实证估计了2003—2016年期间单产、播种面积和结构调整对中国粮食增产的贡献。结果表明,中国粮食实现“十二连增”的巨大成就主要是单产增长贡献,年均贡献率50%以上,播种面积和作物内部结构调整也是不可忽视的重要力量,年均贡献率分别为30%与10%以上。然而,未来中国粮食增产依靠播种面积扩大和结构调整的空间变窄,需要探索新的增产路径。     

Evaluating the Use of Spatial Covariance Structures in the Analysis of Cardiovascular Imaging Data

This article investigates the choice of working covariance structures in the analysis of spatially correlated observations motivated by cardiac imaging data. Through Monte Carlo simulations, we found that the choice of covariance structure affects the efficiency of the estimator and power of the test. Choosing the popular unstructured working covariance structure results in an over-inflated Type I error possibly due to a sample size not large enough relative to the number of parameters being estimated. With regard to model fit indices, Bayesian Information Criterion outperforms Akaike Information Criterion in choosing the correct covariance structure used to generate data.     

Robust Smoothed Rank Estimation Methods for Accelerated Failure Time Model Allowing Clusters

Smoothed Gehan rank estimation methods are widely used in accelerated failure time (AFT) models with/without clusters. However, most methods are sensitive to outliers in the covariates. In order to solve this problem, we propose robust approaches based on the smoothed Gehan rank estimation methods for the AFT model, allowing for clusters by employing two different weight functions. Simulation studies show that the proposed methods outperform existing smoothed rank estimation methods regarding their biases and standard deviations when there are outliers in the covariates. The proposed methods are also applied to a real dataset from the “Major cardiovascular interventions” study.     

Collective versus Individual Effects in Survival Analysis of Multiple Failures

In survival analysis, we sometimes encounter data with multiple censored outcomes. Under certain scenarios, partial or even all covariates have ‘similar’ relative risks on the multiple outcomes in the Cox regression analysis. The similarity in covariate effects can be quantified using the proportionality of regression coefficients. Identifying the proportionality structure, or equivalently whether covariates have individual or collective effects, may have important scientific implications. In addition, it can lead to a smaller set of unknown parameters, which in turn results in more accurate estimation. In this article, we develop a novel approach for identifying the proportionality structure. Simulation shows the satisfactory performance of the proposed approach and its advantage over estimation under no assumed structure. We analyse three datasets to demonstrate the practical application of the proposed approach.     

Intraday Serial Correlation,Volatility, and Jump: Evidence from China's Stock Market

In this article, we investigate the relationships among intraday serial correlation, jump-robust volatility, positive and negative jumps based on Shanghai composite index high frequency data. We implement variance ratio test to quantify intraday serial correlation. We also measure the continuous part of realized volatility using jump-robust MedRV estimator and disentangle positive and negative jumps using Realized Downside Risk Measure and Realized Upside Potential Measure proposed by Bi et al., (2013 Bi, T., Zhang, B., Wu, H. (2013). Measuring downside risk using high frequency data–realized downside risk measure. Communications in Statistics–Simulation and Computation 42(4):741–754.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). We find that intraday serial correlation are positively correlated with jump-robust volatility and negatively correlated with negative jumps which confirm the LeBaron effect.     

Symmetrical Design of Experiment in Global Sensitivity Analysis Based on ANOVA High-dimensional Model Representation

This article reviews symmetrical global sensitivity analysis based on the analysis of variance of high-dimensional model representation. To overcome the computational difficulties and explore the use of symmetrical design of experiment (SDOE), two methods are presented. If the form of the objective function f is known, we use SDOE to estimate the symmetrical global sensitivity indices instead of Monte Carlo or quasi-Monte Carlo simulation. Otherwise, we use the observed values of the experiment to do symmetrical global sensitivity analysis. These methods are easy to implement and can reduce the computational cost. An example is given by symmetrical design of experiment.     

A Proportional Hazards Regression Model for the Subdistribution with Covariates‐adjusted Censoring Weight for Competing Risks Data

With competing risks data, one often needs to assess the treatment and covariate effects on the cumulative incidence function. Fine and Gray proposed a proportional hazards regression model for the subdistribution of a competing risk with the assumption that the censoring distribution and the covariates are independent. Covariate‐dependent censoring sometimes occurs in medical studies. In this paper, we study the proportional hazards regression model for the subdistribution of a competing risk with proper adjustments for covariate‐dependent censoring. We consider a covariate‐adjusted weight function by fitting the Cox model for the censoring distribution and using the predictive probability for each individual. Our simulation study shows that the covariate‐adjusted weight estimator is basically unbiased when the censoring time depends on the covariates, and the covariate‐adjusted weight approach works well for the variance estimator as well. We illustrate our methods with bone marrow transplant data from the Center for International Blood and Marrow Transplant Research. Here, cancer relapse and death in complete remission are two competing risks.