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Rejoinder 反驳
Q4 Mathematics Pub Date : 2023-06-13 DOI: 10.59170/stattrans-2023-034
G. Kalton
I thank the discussants for their kind remarks, for their insightful comments on the present state and future directions of the field, and for the many references they cite. Having no disagreements with them, I will confine my rejoinder to a few issues that their contributions have highlighted for me.
我感谢讨论者的友好发言,感谢他们对该领域的现状和未来方向的深刻评论,以及他们引用的许多参考文献。由于与他们没有任何分歧,我将仅限于他们的贡献为我强调的几个问题。
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引用次数: 0
Quality adjusted GEKS-type indices for price comparisons based on scanner data 质量调整的geks类型指数,用于基于扫描仪数据的价格比较
Q4 Mathematics Pub Date : 2023-06-13 DOI: 10.59170/stattrans-2023-041
Jacek Białek
A wide variety of retailers (supermarkets, home electronics, Internet shops, etc.) provide scanner data containing information at the level of the barcode, e.g. the Global Trade Item Number (GTIN). As scanner data provide complete transaction information, we may use the expenditure shares of items as weightsfor calculating price indices at the lowest (elementary) level of data aggregation. The challenge here is the choice of the index formula which should be able to reduce chain drift bias and substitution bias. Multilateral index methods seem to be the best choice due to the dynamic character of scanner data. These indices work on a wholetime window and are transitive, which is key to the elimination of the chain drift effect. Following what is called an identity test, however, it may be expected that even when only prices return to their original values, the index becomes one. Unfortunately, the commonly used multilateral indices (GEKS, CCDI, GK, TPD, TDH) do not meet the identity test. The paper discusses the proposal of two multilateral indices and their weighted versions. On the one hand, the design of the proposed indices is based on the idea of the GEKS index. On the other hand, similarly to the Geary-Khamis method, it requires quality adjusting. It is shown that the proposed indices meet the identity test and most other tests. In an empirical and simulation study, these indices are compared with the SPQ index, which is relatively new and also meets the identity test. The analytical considerations as well as empirical studies confirm the high usefulness of the proposed indices.
各种各样的零售商(超市、家用电子产品、互联网商店等)提供包含条形码级别信息的扫描仪数据,例如全球贸易商品编号(GTIN)。由于扫描仪数据提供了完整的交易信息,我们可以使用项目的支出份额作为权重,在数据聚合的最低(基本)级别计算价格指数。这里的挑战是指数公式的选择,它应该能够减少链漂移偏差和取代偏差。由于扫描仪数据的动态特性,多边索引方法似乎是最佳选择。这些指数在整个时间窗口上工作,并且是可传递的,这是消除链漂移效应的关键。然而,在所谓的身份测试之后,可以预期,即使只有价格恢复到其原始值,该指数也会成为一个。不幸的是,常用的多边指数(GEKS、CCDI、GK、TPD、TDH)不符合同一性测试。本文讨论了两个多边指数的建议及其加权版本。一方面,所提出的指数的设计是基于GEKS指数的思想。另一方面,与Geary-Khamis方法类似,它需要进行质量调整。结果表明,所提出的指标满足同一性检验和大多数其他检验。在一项实证和模拟研究中,将这些指数与SPQ指数进行了比较,SPQ指数相对较新,也符合同一性检验。分析考虑和实证研究证实了拟议指数的高度有用性。
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引用次数: 0
A nonparametric analysis of discrete time competing risks data: a comparison of the cause-specific-hazards approach and the vertical approach 离散时间竞争风险数据的非参数分析:特定原因风险方法与垂直方法的比较
Q4 Mathematics Pub Date : 2023-06-13 DOI: 10.59170/stattrans-2023-036
Bonginkosi D. Ndlovu, S. Melesse, T. Zewotir
icolaie et al. (2010) have advanced a vertical model as the latest continuous time competing risks model. The main objective of this article is to re-cast this model as a nonparametric model for analysis of discrete time competing risks data. Davis and Lawrance (1989) have advanced a cause-specific-hazard driven method for summarizing discrete time data nonparametrically. The secondary objective of this article is to compare the proposed model to this model. We pay particular attention to the estimates for the cause-specific-hazards and the cumulative incidence functions as well as their respective standard errors.
icolaie等人(2010)提出了一个垂直模型作为最新的连续时间竞争风险模型。本文的主要目的是将该模型重新塑造为一个非参数模型,用于分析离散时间竞争风险数据。Davis和Lawrance(1989)提出了一种基于特定原因的危险驱动方法,用于非框架地总结离散时间数据。本文的次要目的是将所提出的模型与此模型进行比较。我们特别关注特定原因危害的估计值、累积发生率函数及其各自的标准误差。
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引用次数: 0
Models for survey nonresponse and bias adjustment techniques 调查无响应和偏差调整技术模型
Q4 Mathematics Pub Date : 2023-06-13 DOI: 10.59170/stattrans-2023-040
H. O. Ayhan
Survey statisticians have been dealing with the issues of nonresponse in sample surveys for many years. Due to the complex nature of the mechanism, so far it has not been easy to find a general solution to this problem. In this paper, several aspects of this topic will be elaborated on: the survey unit nonresponse bias has been examined alternatively by taking response amounts which are fixed initially and also by taking the response amounts as random variables. An overview of the components of the bias due to nonresponse will be performed. Nonresponse bias components are illustrated for each alternative approach and the amount of bias was computed for each case.
调查统计学家多年来一直在处理抽样调查中的无回复问题。由于机制的复杂性,到目前为止,要找到这个问题的一般解决方案并不容易。在本文中,将详细阐述该主题的几个方面:通过采用最初固定的响应量和将响应量作为随机变量,交替检查了调查单位的无响应偏差。将对因无应答而产生的偏差的组成部分进行概述。说明了每种替代方法的无响应偏差分量,并计算了每种情况的偏差量。
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引用次数: 0
Comments on „Probability vs. Nonprobability Sampling: From the Birth of Survey Sampling to the Present Day” by Graham Kalton 评格雷厄姆·卡尔顿《概率与非概率抽样:从抽样调查的诞生到现在
Q4 Mathematics Pub Date : 2023-06-13 DOI: 10.59170/stattrans-2023-030
D. Pfeffermann
I like to congratulate Professor Kalton for writing this very constructive article on probability versus nonprobability sampling. I learned a lot from reading it. In what follows, I add a few comments on this topic.
我要祝贺卡尔顿教授写了这篇关于概率与非概率抽样的非常有建设性的文章。我从阅读中学到了很多。在下面的文章中,我对这个话题补充了一些评论。
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引用次数: 0
Discussion of “Probability vs. Nonprobability Sampling: From the Birth of Survey Sampling to the Present Day” by Graham Kalton 论格雷厄姆·卡尔顿的《概率与非概率抽样:从调查抽样的诞生到现在
Q4 Mathematics Pub Date : 2023-06-13 DOI: 10.59170/stattrans-2023-033
R. Münnich
Let me first thank Dr. Kalton for his amazing historical review of the development of survey sampling from its origin, contrasting purposive sampling, until now, where some elements of purposive sampling in terms of web or big data seem to supersede the well-elaborated theory of survey statistics. Shall the message be that we do not need any sampling courses at universities anymore, that official statistics should turn to modelling using data with unknown data generating processes, or actually even be substituted by (commercial) data krakens? Hardly so! Graham Kalton emphasises a modern thinking about the use of these new data sources which may also have some advantages and he urges future research on data integration methods using (very) different kinds of data while strongly taking quality aspects into account.
首先,我要感谢Kalton博士对调查抽样从起源到发展的惊人历史回顾,对比目的性抽样,直到现在,在网络或大数据方面,目的性抽样的一些元素似乎取代了精心设计的调查统计理论。是否应该传达这样的信息:我们不再需要大学里的任何抽样课程,官方统计应该转向使用未知数据生成过程的数据建模,或者实际上甚至被(商业)数据破解器所取代?几乎所以!Graham Kalton强调使用这些新数据源的现代思维可能也有一些优势,他敦促未来研究使用(非常)不同类型的数据的数据集成方法,同时强烈考虑质量方面。
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引用次数: 0
Bayesian modelling for semi-competing risks data in the presence of censoring 审查条件下半竞争风险数据的贝叶斯建模
Q4 Mathematics Pub Date : 2023-06-13 DOI: 10.59170/stattrans-2023-044
A. Bhattacharjee, Rajashree Dey
In biomedical research, challenges to working with multiple events are often observed while dealing with time-to-event data. Studies on prolonged survival duration are prone to having numerous possibilities. In studies on prolonged survival, patients might die of other causes. Sometimes in the survival studies, patients experienced some events (e.g. cancer relapse) before dying within the study period. In this context, the semi-competing risks framework was found useful. Similarly, the prolonged duration of follow-up studies is also affected by censored observation, especially interval censoring, and right censoring. Some conventional approaches work with time-to-event data, like the Cox-proportional hazard model. However, the accelerated failure time (AFT) model is more effective than the Cox model because it overcomes the proportionality hazard assumption. We also observed covariates impacting the time-to-event data measured as the categorical format. No established method currently exists for fitting an AFT model that incorporates categorical covariates, multiple events, and censored observations simultaneously. This work is dedicated to overcoming the existing challenges by the applications of R programming and data illustration. We arrived at a conclusion that the developed methods are suitable to run and easy to implement in R software. The selection of covariates in the AFT model can be evaluated using model selection criteria such as the Deviance Information Criteria (DIC) and Log-pseudo marginal likelihood (LPML). Various extensions of the AFT model, such as AFT-DPM and AFT-LN, have been demonstrated. The final model was selected based on minimum DIC values and larger LPML values.
在生物医学研究中,在处理时间到事件的数据时,经常会观察到处理多个事件的挑战。关于延长生存期的研究有很多可能性。在延长生存期的研究中,患者可能死于其他原因。有时,在生存研究中,患者在研究期内死亡前经历了一些事件(如癌症复发)。在这方面,半竞争性风险框架被认为是有用的。同样,随访研究的持续时间延长也受到审查观察的影响,尤其是区间审查和右审查。一些传统的方法处理事件时间数据,如Cox比例风险模型。然而,加速失效时间(AFT)模型比Cox模型更有效,因为它克服了比例风险假设。我们还观察到协变量影响作为分类格式测量的事件时间数据。目前还没有建立的方法来拟合同时包含分类协变量、多个事件和截尾观测的AFT模型。这项工作致力于通过应用R编程和数据说明来克服现有的挑战。我们得出的结论是,所开发的方法适合在R软件中运行,并且易于实现。AFT模型中协变量的选择可以使用模型选择标准来评估,例如偏差信息标准(DIC)和对数伪边际似然(LPML)。AFT模型的各种扩展,如AFT-DPM和AFT-LN。基于最小DIC值和较大LPML值来选择最终模型。
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引用次数: 0
Rotation schemes and Chebyshev polynomials 旋转格式与Chebyshev多项式
Q4 Mathematics Pub Date : 2023-06-13 DOI: 10.59170/stattrans-2023-035
J. Wesołowski
There is a continuing interplay between mathematics and survey methodology involving different branches of mathematics, not only probability. This interplay is quite obvious as regards the first of the two options: probability vs. non-probability sampling, as proposed and discussed in Kalton (2023). There, mathematics is represented by probability and mathematical statistics. However, sometimes connections between mathematics and survey methodology are less obvious, yet still crucial and intriguing. In this paper we refer to such an unexpected relation, namely between rotation sampling and Chebyshev polynomials. This connection, introduced in Kowalski and Wesołowski (2015), proved fundamental for the derivation of an explicit form of the recursion for the BLUE µˆt of the mean on each occasion t in repeated surveys based on a cascade rotation scheme. This general result was obtained under two basic assumptions: ASSUMPTION I and ASSUMPTION II, expressed in terms of the Chebyshev polynomials. Moreover, in that paper, it was conjectured that these two assumptions are always satisfied, so the derived form of recursion is universally valid. In this paper, we partially confirm this conjecture by showing that ASSUMPTION I is satisfied for rotation patterns with a single gap of an arbitrary size.
数学和调查方法之间有持续的相互作用,涉及不同的数学分支,而不仅仅是概率。Kalton(2023)提出并讨论了两种选择中的第一种:概率与非概率抽样,这种相互作用非常明显。在那里,数学是由概率和数理统计来表示的。然而,有时数学和调查方法之间的联系不那么明显,但仍然是至关重要和有趣的。在本文中,我们提到了这样一种意想不到的关系,即旋转采样与切比雪夫多项式之间的关系。在Kowalski和Wesołowski(2015)中介绍的这种联系,证明了在基于级联旋转方案的重复调查中,每次t的平均值的BLUE μ t递归的显式形式推导的基础。这个一般结果是在两个基本假设下得到的:假设1和假设2,用切比雪夫多项式表示。此外,文中还推测这两个假设总是满足的,因此推导出的递归形式是普遍有效的。本文通过证明假设1对于任意大小的单间隙旋转模式是满足的,部分地证实了这一猜想。
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引用次数: 0
Bayesian estimation of a geometric distribution using informative priors based on a Type-I censoring scheme 基于I型截尾方案的基于信息先验的几何分布的贝叶斯估计
Q4 Mathematics Pub Date : 2023-06-13 DOI: 10.59170/stattrans-2023-047
Nadeem Akhtar, S. Khan, Muhammad Amin, Akbar Ali Khan, Amjad Ali, Sadaf Manzoor
In this paper, the geometric distribution parameter is estimated under a type-I censoring scheme by means of the Bayesian estimation approach. The Beta and Kumaraswamy informative priors, as well as five loss functions are used for this purpose. Expressions of Bayes estimators and Bayes risks are derived under the Squared Error Loss Function (SELF), the Quadratic Loss Function (QLF), the Precautionary Loss Function (PLF), the Simple Asymmetric Precautionary Loss Function (SAPLF), and the DeGroot Loss Function (DLF) using the two aforementioned priors. The prior densities are obtained through prior predictive distributions. Simulation studies are carried out to make comparisons using Bayes risks. Finally, a real-life data example is used to verify the model’s efficiency.
本文利用贝叶斯估计方法,在I型截尾方案下估计几何分布参数。Beta和Kumaraswamy信息先验以及五个损失函数用于此目的。贝叶斯估计量和贝叶斯风险的表达式是在平方误差损失函数(SELF)、二次损失函数(QLF)、预防性损失函数(PLF)、简单不对称预防性损失功能(SAPLF)和DeGroot损失函数(DLF)下使用上述两个先验推导的。先验密度是通过先验预测分布获得的。进行模拟研究以使用贝叶斯风险进行比较。最后,以实际数据为例验证了模型的有效性。
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引用次数: 0
Estimating the probability of leaving unemployment for older people in Poland using survival models with censored data 使用带有删节数据的生存模型估计波兰老年人失业的可能性
Q4 Mathematics Pub Date : 2023-06-13 DOI: 10.59170/stattrans-2023-046
Wioletta Grzenda
Current demographic changes require greater participation of people aged 50 or older in the labour market. Previous research shows that the chances of returning to employment decrease with the length of the unemployment period. In the case of older people who have not reached the statutory retirement age, these chances also depend on the time they have left to retirement. Our study aims to assess the probability of leaving unemployment for people aged 50-71 based on their characteristics and the length of the unemployment period. We use data from the Labour Force Survey for 2019–2020. The key factors determining employment status are identified using the proportional hazard model. We take these factors into account and use the direct adjusted survival curve to show how the probability of returning to work in Poland changes as people age. Due to the fact that not many people take up employment around their retirement age, an in-depth evaluation of the accuracy of predictions obtained via the models is crucial to assess the results. Hence, in this paper, a time-dependent ROC curve is used. Our results indicate that the key factor that influences the return to work after an unemployment period in the case of older people in Poland is whether they reached the age of 60. Other factors that proved important in this context are the sex and the education level of older people.
当前的人口结构变化要求50岁或50岁以上的人更多地参与劳动力市场。先前的研究表明,重新就业的机会随着失业期的延长而减少。对于未达到法定退休年龄的老年人来说,这些机会也取决于他们退休的剩余时间。我们的研究旨在根据50-71岁人群的特点和失业期的长短来评估他们失业的可能性。我们使用了2019-2020年劳动力调查的数据。使用比例风险模型确定了决定就业状况的关键因素。我们将这些因素考虑在内,并使用直接调整后的生存曲线来显示波兰重返工作岗位的概率如何随着年龄的增长而变化。由于没有多少人在退休年龄前后就业,因此深入评估通过模型获得的预测的准确性对于评估结果至关重要。因此,在本文中,使用了一条与时间相关的ROC曲线。我们的研究结果表明,影响波兰老年人失业期后重返工作岗位的关键因素是他们是否达到60岁。在这方面证明重要的其他因素是老年人的性别和教育水平。
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引用次数: 0
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Statistics in Transition
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