An information-theoretic approach to effective inference for Z-functionals

In this paper, through an information-theoretic approach, we construct estimations and confidence intervals of Z-functionals involving finite population and with the presence of auxiliary information. In particular, we give a method of estimating the variance of finite population with known mean. The modified estimates and confidence intervals for Z-functionals can adequately use the auxiliary information, at least not worse than what the standard ones do. A simulation study is presented to assess the performance of the modified estimates for the finite sample case.     

关于洛伦兹曲线和基尼系数的统计推断

本文对于洛伦兹曲线的最一般定义,在无任何附加限制条件下,论证了基于样本数据所得到的洛仑兹曲线的通常估计量具有强相合性.在此基础上,证明了基尼系数和Schutz系数的通常估计量均具有强相合性.此外,导出了基尼系数估计量的渐进分布,并在此基础上给出了大样本情形下基尼系数的置信区间.     

CONSENSUS FORMATION OF TWO-LEVEL OPINION DYNAMICS

Opinion dynamics have received significant attention in recent years. This paper proposes a bounded confidence opinion model for a group of agents with two different confidence levels. Each agent in the population is endowed with a confidence interval around her opinion with radius αd or(1- α)d, where α∈(0, 1/2] represents the differentiation of confidence levels. We analytically derived the critical confidence bound dc = 1/(4α) for the two-level opinion dynamics on Z. A single opinion cluster is formed with probability 1 above this critical value regardless of the ratio p of agents with high/low confidence. Extensive numerical simulations are performed to illustrate our theoretical results. Noticed is a clear impact of p on the collective behavior: more agents with high confidence lead to harder agreement. It is also experimentally revealed that the sharpness of the threshold dc increases with α but does not depend on p.     

近红外全局隐含温度补偿模型的预测精度分析

温度波动影响含氢基团之间的作用力,从而影响近红外光谱的吸收强度和波峰位置等,导致近红外测量精度的降低。针对温度变化对近红外光谱建模精度的影响,对全局隐含温度补偿方法进行了研究,并对其预测精度进行了分析,分别从预测方差和置信区间两个方面对此类模型的精度进行了理论探讨和验证。同时通过温度的连续变化实验,即在温度连续变化的过程中,等时间间隔采集各样品的近红外光谱,研究了温度变化对光谱主元的连续模式影响,探讨了温度变化影响模型预测精度的方式和途径。最后对某高分子聚合物的粘度测量问题进行了实验验证和误差分析,得到标准温度下所建未经温度补偿的模型和全局隐含温度补偿模型的建模精度分别为：RMSEC=0.243 0, R_c=0.871 6, RMSEP=0.243 2, R_p=0.869 3; RMSEC=0.258 2, R_c=0.870 6, RMSEP=0.265 2, R_p=0.856 0,而当温度变化时,二者预测最大置信区间分别约为1.8和0.9 kPa·s。虽然全局隐含温度补偿模型相比于标准温度模型建模精度略降低,但预测精度提高了一倍左右。理论分析和实验结果均表明,全局温度补偿模型具有较高的预测精度,且对温度的变化有较强的鲁棒性和可靠性。     

分层含结构零2×2列联表基于风险比的同时置信区间估计

对分层含结构零2×2列联表中风险比的同时置信区间估计问题,提出五种基于似然比统计量、Score统计量、Wald统计量和对数变换Wald统计量的同时置信区间及三种Bootstrap同时置信区间。并采用Bonferroni,Single-step adjusted MaxT和Single-step adjusted MinP三种多重检验过程计算临界值。通过同时置信区间覆盖概率、覆盖宽度和Mesial非覆盖概率与非覆盖概率之比(RNCP)的模拟研究比较了置信区间的统计性能。结果表明,MinP检验过程下基于Score统计量的同时置信区间具有令人满意的结果,即这个区间的覆盖概率非常接近置信水平,且Mesial非覆盖概率与非覆盖概率之比(RNCP)均在[0.4,0.6]之间。最后通过实例分析对所提方法进行验证。     

条件分位数和条件密度的经验似然置信区间

本文首次把经验似然引入非参数回归模型，分别得到了条件分位数和条件密度的经验似然置信区间。