High-Accuracy Confidence Regions for Distribution Parameters

With the help of today’s computers, it is always relatively easy to find maximum-likelihood estimators of one or more parameters of any specific statistical distribution, and use these to construct the corresponding approximate confidence interval/region, facilitated by the well-known asymptotic properties of the likelihood function. The purpose of this article is to make this approximation substantially more accurate by extending the Taylor expansion of the corresponding probability density function to include quadratic and cubic terms in several centralized sample means, and thus finding the corresponding -proportional correction to the original algorithm. We then demonstrate the new procedure’s usage, both for constructing confidence regions and for testing hypotheses, emphasizing that incorporating this correction carries minimal computational and programming cost. In our final chapter, we present two examples to indicate how significantly the new approximation improves the procedure’s accuracy.

ON CONFIDENCE REGIONS OF SEMIPARAMETRIC NONLINEAR REGRESSION MODELS(A GEOMETRIC APPROACH)

A geometric framework is proposed for semiparametric nonlinear regression models based on the concept of least favorable curve, introduced by Severini and Wong (1992). The authors use this framework to drive three kinds of improved approximate confidence regions for the parameter and parameter subset in terms of curvatures. The results obtained by Hamilton et al. (1982), Hamilton (1986) and Wei (1994) are extended to semiparametric nonlinear regression models.

CONFIDENCE REGIONS IN TERMS OF STATISTICAL CURVATURE FOR AR(q) NONLINEAR REGRESSION MODELS

This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence regions for parameters and parameter subsets in terms of statistical curvatures are given based on the likelihood ratio statistics and score statistics. Several previous results, such as [1] and [2] are extended to AR(q) nonlinear regression models.

Joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples

In this paper, we obtain the joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples. As an application of this result, the empirical likelihood confidence intervals for the difference of any two quantiles are also obtained.

Confidence Regions with Nuisance Parameters

Consider a distribution with several parameters whose exact values are unknown and need to be estimated using the maximum-likelihood technique. Under a regular case of estimation, it is fairly routine to construct a confidence region for all such parameters, based on the natural logarithm of the corresponding likelihood function. In this article, we investigate the case of doing this for only some of these parameters, assuming that the remaining (so called nuisance) parameters are of no interest to us. This is to be done at a chosen level of confidence, maintaining the usual accuracy of this procedure (resulting in about 1% error for samples of size , and further decreasing with 1/n). We provide a general solution to this problem, demonstrating it by many explicit examples.

Data Assimilation Method Based on the Constraints of Confidence Region

The ensemble Kalman filter （EnKF） is a distinguished data assimilation method that is widely used and studied in various fields including methodology and oceanography. However, due to the limited sample size or imprecise dynamics model, it is usually easy for the forecast error variance to be underestimated, which further leads to the phenomenon of filter divergence. Additionally, the assimilation results of the initial stage are poor if the initial condition settings differ greatly from the true initial state. To address these problems, the variance inflation procedure is usually adopted. In this paper, we propose a new method based on the constraints of a confidence region constructed by the observations, called EnCR, to estimate the inflation parameter of the forecast error variance of the EnKF method. In the new method, the state estimate is more robust to both the inaccurate forecast models and initial condition settings. The new method is compared with other adaptive data assimilation methods in the Lorenz-63 and Lorenz-96 models under various model parameter settings. The simulation results show that the new method performs better than the competing methods.

A Non-Asymptotic Confidence Region with a Fixed Size for a Scalar Function Value: Applications in C-OTDR Monitoring Systems

In this paper we will investigate some non-asymptotic properties of the modified least squares estimates for the non-linear function f(λ*) by observations that nonlinearly depend on the parameter λ*. Non-asymptotic confidence regions with fixed sizes for the modified least squares estimate are used. The obtained confidence region is valid for a finite number of data points when the distributions of the observations are unknown. Asymptotically the suggested estimates represent usual estimates of the least squares. The paper presents the results of practical applications of the proposed method in C-OTDR monitoring systems.

多元广义线性模型经验似然方法分析

针对多元广义线性模型,基于估计相关阵、广义估计方程和经验似然方法,本文构造出经验似然比统计量,此统计量能克服“工作相关阵”方法的误设定问题.在一定的条件下,本文也获得了经验似然比统计量渐近Wilks性质,该结果可用作未知参数向量置信域的构造.最后,通过数值模拟对所提方法的有效性进行验证.

地域文化在培养大学生“家国情怀”中的作用及实施路径

家国情怀是人们对故土的眷念,是个体对家庭的依恋,是个人对国家的归属情感、价值认同和责任担当,是一种深层的文化心理密码。具有丰富内涵和人文价值的地域文化对于大学生家国情怀的培养有重要作用。优秀的地域文化有利于大学生习得当地的风俗习惯,形成对地域文化的认同感,从而有利于提高大学生的地方文化传承和传播能力,增强大学生的文化自信。地域文化应该通过进入高校课堂、融入课程思政,营造校园文化环境,构建文化育人体系,开展社会实践活动,融入学校科研平台等措施,发挥其独特的培养大学生家国情怀的作用。

基于区域分割和DM642的数字图像修复系统研究

由于数字图像中颜色通道之间关联性显著,改变某颜色分量,会导致剩余分量随之变化,使数字图像整体视觉效果出现变化,针对该问题,文中研究基于区域分割和DM642的数字图像修复系统。将DM642处理器作为系统核心处理器,在该处理器协助下,针对破损数字图像采用基于分通道自体理论的数字图像区域分割方法,利用图像颜色信息和像素间的空间关系,实现图像修复区域分割。针对需修复区域,通过基于Criminisi算法的数字图像修复方法提取修复像素点生成修复块,利用图像自相似性,在未破损区域找到与修复块匹配度最高的样本块,用此样本填充修补破损区域。实验结果表明,此系统能够有效分割数字图像的修复区域,修复视觉效果较好,且修复后数字图像不存在明显失真问题,可实现多图像并行快速修复。

文旅融合背景下安康地域文化传承创新研究

“旅游是文化的重要载体和平台,文化乃旅游之灵魂。”丰富多样的地域文化是旅游文化的重要组成部分之一。为更好地彰显“以文兴旅、以旅彰文”理念,该文以安康地域文化的传承为研究内容,采用文献查阅法、调查研究法,系统梳理了安康地域文化的独特魅力,归纳总结了安康地域文化的内涵,认识到文旅融合背景下传承创新安康地域文化乃塑造旅游文化的灵魂,并提出从“生态+文旅”“毛绒玩具+文旅”“非遗+文旅”“美食+文旅”等模式多层面提升安康文旅品牌效应,传承创新地域文化,深化文旅融合发展,为经济社会发展赋能,推动文化繁荣、坚定文化自信。

Empirical likelihood confidence regions of the parameters in a partially linear single-index model

In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.

GENERALIZED CONFIDENCE REGIONS OF FIXED EFFECTS IN THE TWO-WAY ANOVA

作者在 heteroscedasticity 下面讨论失衡的双向 ANOVA 模型。由采取概括途径，作者为为这些效果测试固定效果和概括信心区域的平等导出概括 p 值。作者也在大样品的情况中提供他们的 frequentist 性质。模拟研究证明概括信心区域有好范围可能性。

Joint Empirical Likelihood Confidence Regions for a Finite Number of Quantiles Under Negatively Associated Samples

In this paper, the authors obtain the joint empirical likelihood con?dence regions for a?nite number of quantiles under negatively associated samples. As an application of this result, the empirical likelihood con?dence intervals for the difference of any two quantiles are also developed.

NA样本下随机设计情形部分线性模型的经验似然推断

本文研究NA样本下随机设计情形部分线性模型的经验似然推断,将分块技术应用到经验似然方法中,证明部分线性模型的参数β的对数经验似然比统计量的渐近分布为卡方分布,由此构造了NA样本下β的经验似然置信区间.同时,在有限样本情况下给出运用分块技术的经验似然与不运用分块技术的经验似然的模拟对比结果.

湖南地区应力场定量结果及置信区间分析

基于湖南及其邻区312个地震的529条P波初动极性数据和32个M_(L)≥2.8地震的震源机制解,采用格点尝试法和网格搜索法分别反演得到了湖南地区构造应力场的定量结果和置信范围。格点尝试法计算得到的P轴方位和倾伏角分别为102°和10°,T轴方位和倾伏角分别为237°和76°;网格搜索法反演得到的P轴方位和倾伏角分别为100°(置信区间为79°~100°)和5°(置信区间为2°~5°),T轴方位和倾伏角分别为225°(置信区间为204°~225°)和81°(置信区间为81°~82°)。结果表明:湖南地区平均震源机制解表现为逆断型;主压应力轴优势方位为NWW向,倾伏角近乎水平;主张应力轴优势方位为NE—NEE向,倾伏角较大。对两种方法得到的研究区应力场结果进行了可靠性分析并与前人结果进行了对比,证实本文结果的可信度较高。

《典籍里的中国》创新传播的文化价值研究

《典籍里的中国》是整合主流媒体和学界、演艺界等各方力量,连接传统文化和创新文化,放大资源优势和传播影响力,而推出的全媒体创新表达的一档传播新样态的文化类节目。其创新传播的文化价值在于助力文化强国建设,加持中华民族的身份认知自觉、国家地域意识自觉、民族文化基因自觉和“命运共同体”多重典范自觉。

地域文化与城市性格的抒写——评聂还贵《雕刻在石头上的王朝》

聂还贵的作品立足于地域的历史文化,长篇学术散文《雕刻在石头上的王朝》揭开了北魏历史及云冈石窟的神秘面纱,对古都大同的历史文化进行多维透视与关照,具有强烈的地域文化认同感;作者挖掘北魏史料,探寻历史人物深处的人性,同时也抒写出一座城市的性格与灵魂,建构起城市独有的文化自信。

基于轻量化区域置信网络的细粒度图像分类

为提高细粒度图像分类的准确率和速度,提出区域投票分类模型和区域置信度机制以及基于轻量化区域置信网络的细粒度图像分类方法。将轻量化卷积神经网络分类器替换为区域投票分类器,加入区域置信机制,增加分类网络对于关键特征分类的权重,提升轻量化模型的准确率。在Cub200-2011数据集上的实验结果验证了区域投票模型和区域置信机制的有效性。相较于其它主流细粒度图像分类算法,改进后的模型仅损失了少量精度,却大幅减少了参数量和所需运算资源。

EMPIRICAL LIKELIHOOD CONFIDENCE REGION FOR PARAMETERS IN LINEAR ERRORS-IN-VARIABLES MODELS WITH MISSING DATA

multivariate 线性 errors-in-variables 模型 regressors 什么时候在在 Rubin (1976 ) 的意义的随机是失踪的，在这份报纸被考虑。为 0 在这建模的一个参数的一个抑制实验可能性的信心区域被建议，它被基于反的概率把相应于加权的摆平的直角的距离的 20 个函数与 0 的一个抑制区域相结合构造。在真参数的实验木头可能性的比率收敛到标准 chi 平方分发，这被显示出。模拟证明建议信心区域的范围率接近名字的水平，信心间隔的长度是比反的概率的正常近似的那些狭窄的在大多数情况中的加权的调整最不方形的评估者。一个真实例子被学习，结果支持理论和模拟结论。