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Point process modeling through a mixture of homogeneous and self-exciting processes 通过同质和自激过程的混合物进行点过程建模
IF 1.5 3区 数学 Q2 STATISTICS & PROBABILITY Pub Date : 2024-01-15 DOI: 10.1111/stan.12334
Álvaro Briz-Redón, Jorge Mateu
Self-exciting point processes allow modeling the temporal location of an event of interest, considering the history provided by previously observed events. This family of point processes is commonly used in several areas such as criminology, economics, or seismology, among others. The standard formulation of the self-exciting process implies assuming that the underlying stochastic process is dependent on its previous history over the entire period under analysis. In this paper, we consider the possibility of modeling a point pattern through a point process whose structure is not necessarily of self-exciting type at every instant or temporal interval. Specifically, we propose a mixture point process model that allows the point process to be either self-exciting or homogeneous Poisson, depending on the instant within the study period. The performance of this model is evaluated both through a simulation study and a case study. The results indicate that the model is able to detect the presence of instants in time, referred to as change points, where the nature of the process varies.
自激点过程可以对感兴趣事件的时间位置进行建模,同时考虑到之前观测到的事件所提供的历史。这一系列点过程通常用于犯罪学、经济学或地震学等多个领域。自激过程的标准表述意味着假设基本随机过程在整个分析期间都依赖于其先前的历史。在本文中,我们考虑了通过点过程对点模式进行建模的可能性,该点过程的结构并不一定在每个瞬间或时间间隔内都属于自激类型。具体来说,我们提出了一种混合点过程模型,该模型允许点过程为自激或同质泊松,具体取决于研究时段内的瞬间。我们通过模拟研究和案例研究对该模型的性能进行了评估。结果表明,该模型能够检测到时间中存在过程性质发生变化的瞬间(称为变化点)。
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引用次数: 0
The concept of sufficiency in conditional frequentist inference 条件频率论推理中的充分性概念
IF 1.5 3区 数学 Q2 STATISTICS & PROBABILITY Pub Date : 2023-12-02 DOI: 10.1111/stan.12333
Paul Kabaila, A. H. Welsh
We consider inference about the parameter that determines the distribution of the data. In frequentist inference a very important and useful idea is that data reduction to a sufficient statistic does not lose any information about this parameter. We recall two justifications for this idea in frequentist inference. We then examine the extent to which these justifications carry over to conditional frequentist inference inference, which consists of carrying out frequentist inference conditional on an ancillary statistic. This examination shows that, in the context of conditional frequentist inference, first reducing data to a sufficient statistic is not always justified, so we should first condition on an ancillary statistic. Finally, we describe two types of practically-important statistical models that illustrate this finding.
我们考虑关于决定数据分布的参数的推断。在频率推断中,一个非常重要和有用的思想是,将数据约简为一个充分的统计量不会丢失关于该参数的任何信息。我们回想起在频率论推理中对这一观点的两个证明。然后,我们检查这些论证延续到条件频率推理推理的程度,这包括在辅助统计上执行频率推理的条件。这一检验表明,在条件频率推理的背景下,首先将数据简化为充分统计量并不总是合理的,因此我们应该首先对辅助统计量进行条件。最后,我们描述了两种实际重要的统计模型来说明这一发现。
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引用次数: 0
Marginal Log‐linear Parameters and their Collapsibility for Categorical Data 分类数据的边际对数线性参数及其可折叠性
3区 数学 Q2 STATISTICS & PROBABILITY Pub Date : 2023-11-13 DOI: 10.1111/stan.12332
S. Ghosh, P. Vellaisamy
Collapsibility is a practical and useful technique for dimension reduction in multidimensional contingency tables. In this paper, we consider marginal log‐linear models for studying collapsibility and related aspects in such tables. These models generalize ordinary log‐linear and multivariate logistic models, besides several others. First, we obtain some characteristic properties of marginal log‐linear parameters. Then we define collapsibility and strict collapsibility of these parameters in a general sense. Several necessary and sufficient conditions for collapsibility and strict collapsibility are derived based on simple functions of only the cell probabilities, which are easily verifiable. These include results for an arbitrary set of marginal log‐linear parameters having some common effects. The connections of strict collapsibility to various forms of independence of the variables are explored. We analyze some real‐life datasets to illustrate the above results on collapsibility and strict collapsibility. Finally, we obtain a result relating parameters with the same effect, but different margins for an arbitrary table, and demonstrate smoothness of marginal log‐linear models under collapsibility conditions. This article is protected by copyright. All rights reserved.
折叠性是一种实用的多维列联表降维技术。在本文中,我们考虑边际对数线性模型来研究这种表的可折叠性和相关方面。这些模型推广了普通的对数线性和多元逻辑模型,以及其他一些模型。首先,我们得到了边际对数线性参数的一些特征性质。然后在一般意义上定义了这些参数的可折叠性和严格可折叠性。从单元概率的简单函数出发,导出了可折叠性和严格可折叠性的几个充分必要条件,这些条件易于验证。这些结果包括具有一些共同效应的任意一组边际对数线性参数的结果。探讨了严格可折叠性与各种形式的变量独立性之间的联系。我们分析了一些实际数据集来说明上述关于可折叠性和严格可折叠性的结果。最后,我们得到了一个关于任意表的参数具有相同效果,但边界不同的结果,并证明了边际对数线性模型在可折叠性条件下的平滑性。这篇文章受版权保护。版权所有。
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引用次数: 1
Generalized K‐Variate Proportional Hazard Function For Censored Survival Data 截尾生存数据的广义K变量比例风险函数
3区 数学 Q2 STATISTICS & PROBABILITY Pub Date : 2023-11-10 DOI: 10.1111/stan.12327
Hilmi Fadel Kittani
This note develops a generalized ‐variate hazard function for censored data in survival analysis. It introduces a generalized recursive formula, extending the bivariate and trivariate cases introduced by Clayton and Cuzick (1985, Journal of the Royal Statistical Society: Series A (General) , 148(2):82–108) and Kittani (1995, Journal of Mathematical Sciences , 67–74), respectively. The newly developed function is explicitly specified by association parameters and marginal hazard functions.
本文发展了生存分析中截尾数据的广义变量风险函数。它引入了一个广义的递归公式,扩展了Clayton和Cuzick (1985, Journal of Royal Statistical Society: Series a (General), 148(2): 82-108)和Kittani (1995, Journal of Mathematical Sciences, 67-74)分别介绍的二元和三变量情况。该函数由关联参数和边际风险函数明确表示。
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引用次数: 0
Asymptotic approximations of expectations of power means 幂均值期望的渐近逼近
3区 数学 Q2 STATISTICS & PROBABILITY Pub Date : 2023-11-08 DOI: 10.1111/stan.12331
Tomislav Buri, Lenka Mihokovi
Abstract In this paper we study how the expectations of power means behave asymptotically as some relevant parameter approaches infinity and how to approximate them accurately for general non‐negative continuous probability distributions. We derive approximation formulae for such expectations as distribution mean increases, and apply them to some commonly used distributions in statistics and financial mathematics. By numerical computations we demonstrate the accuracy of the proposed formulae which behave well even for smaller sample sizes. Furthermore, analysis of behaviour depending on sample size contributes to interesting connections with the power mean of probability distribution. This article is protected by copyright. All rights reserved.
摘要本文研究了一般非负连续概率分布的幂均值期望值在相关参数趋于无穷时的渐近性,以及如何精确地逼近它们。本文推导了分布均值增加期望值的近似公式,并将其应用于统计和金融数学中一些常用的分布。通过数值计算,我们证明了所提出公式的准确性,即使在较小的样本量下也表现良好。此外,根据样本量对行为进行分析有助于与概率分布的幂均值建立有趣的联系。这篇文章受版权保护。版权所有。
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引用次数: 0
Scaling priors for Intrinsic Gaussian Markov Random Fields applied to blood pressure data 内禀高斯马尔可夫随机场的尺度先验应用于血压数据
3区 数学 Q2 STATISTICS & PROBABILITY Pub Date : 2023-11-06 DOI: 10.1111/stan.12330
Maria‐Zafeiria Spyropoulou, James Bentham
An Intrinsic Gaussian Markov Random Field (IGMRF) can be used to induce conditional dependence in Bayesian hierarchical models. IGMRFs have both a precision matrix, which defines the neighborhood structure of the model, and a precision, or scaling, parameter. Previous studies have shown the importance of selecting the prior for this scaling parameter appropriately for different types of IGMRF, as it can have a substantial impact on posterior estimates. Here, we focus on cases in one and two dimensions, where tuning of the prior is achieved by mapping it to the marginal SD of an IGMRF of corresponding dimensionality. We compare the effects of scaling various IGMRFs, including an application to real two‐dimensional blood pressure data using MCMC methods.
一个内禀高斯马尔可夫随机场(IGMRF)可以用来诱导贝叶斯层次模型中的条件依赖。igmrf既有精度矩阵(定义模型的邻域结构),也有精度或缩放参数。先前的研究表明,为不同类型的IGMRF适当地选择该缩放参数的先验是很重要的,因为它可以对后验估计产生重大影响。在这里,我们关注一维和二维的情况,其中先验的调整是通过将其映射到相应维数的IGMRF的边际SD来实现的。我们比较了缩放各种igmrf的效果,包括使用MCMC方法对真实二维血压数据的应用。
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引用次数: 0
Forecasting Performance of Machine Learning, Time Series and Hybrid Methods for Low and High Frequency Time Series 机器学习、时间序列和混合方法对低频和高频时间序列的预测性能
3区 数学 Q2 STATISTICS & PROBABILITY Pub Date : 2023-11-03 DOI: 10.1111/stan.12326
Ozancan Ozdemir, Ceylan Yozgatlıgil
One of the main objectives of the time series analysis is forecasting, so both Machine Learning methods and statistical methods have been proposed in the literature. In this study, we compare the forecasting performance of some of these approaches. In addition to traditional forecasting methods, which are the Naive and Seasonal Naive Methods, S/ARIMA, Exponential Smoothing, TBATS, Bayesian Exponential Smoothing Models with Trend Modifications and STL Decomposition, the forecasts are also obtained using seven different machine learning methods, which are Random Forest, Support Vector Regression, XGBoosting, BNN, RNN, LSTM, and FFNN, and the hybridization of both statistical time series and machine learning methods. The data set is selected proportionally from various time domains in M4 Competition data set. Thereby, we aim to create a forecasting guide by considering different preprocessing approaches, methods, and data sets having various time domains. After the experiment, the performance and impact of all methods are discussed. Therefore, most of the best models are mainly selected from machine learning methods for forecasting. Moreover, the forecasting performance of the model is affected by both the time frequency and forecast horizon. Lastly, the study suggests that the hybrid approach is not always the best model for forecasting. Hence, this study provides guidelines to understand which method will perform better at different time series frequencies.
时间序列分析的主要目标之一是预测,因此文献中提出了机器学习方法和统计方法。在本研究中,我们比较了其中一些方法的预测性能。除了传统的朴素法和季节朴素法、S/ARIMA、指数平滑、TBATS、趋势修正贝叶斯指数平滑模型和STL分解等预测方法外,还采用随机森林、支持向量回归、XGBoosting、BNN、RNN、LSTM和FFNN等7种不同的机器学习方法,以及统计时间序列和机器学习方法的混合方法进行预测。数据集是按比例从M4比赛数据集中的各个时域中选择的。因此,我们的目标是通过考虑不同的预处理方法、方法和具有不同时域的数据集来创建一个预测指南。通过实验,讨论了各种方法的性能和影响。因此,大多数最好的模型主要是从机器学习方法中选择的。此外,模型的预测效果受时间频率和预测范围的影响。最后,研究表明,混合方法并不总是预测的最佳模型。因此,本研究提供了指导方针,以了解哪种方法在不同的时间序列频率下表现更好。
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引用次数: 0
Asymptotic comparison of negative multinomial and multivariate normal experiments 负多项与多元正态实验的渐近比较
3区 数学 Q2 STATISTICS & PROBABILITY Pub Date : 2023-10-30 DOI: 10.1111/stan.12328
Christian Genest, Frédéric Ouimet
This note presents a refined local approximation for the logarithm of the ratio between the negative multinomial probability mass function and a multivariate normal density, both having the same mean–covariance structure. This approximation, which is derived using Stirling's formula and a meticulous treatment of Taylor expansions, yields an upper bound on the Hellinger distance between the jittered negative multinomial distribution and the corresponding multivariate normal distribution. Upper bounds on the Le Cam distance between negative multinomial and multivariate normal experiments ensue.
本文提出了负多项概率质量函数与多元正态密度之间的比率的对数的精细局部近似,两者具有相同的均值协方差结构。这个近似是用斯特林公式和对泰勒展开的细致处理推导出来的,它给出了抖动负多项分布和相应的多元正态分布之间的海灵格距离的上界。负多项式和多元正态实验之间的Le Cam距离的上界随之而来。
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引用次数: 1
New article types in Statistica Neerlandica 新文章类型在统计荷兰
3区 数学 Q2 STATISTICS & PROBABILITY Pub Date : 2023-10-17 DOI: 10.1111/stan.12324
Ernst‐Jan Camiel Wit
In May 2023 a new editorial team, consisting of Edwin van den Heuvel, Veronica Vinciotti and myself, Ernst Wit, currently with the help of Casper Albers, have taken over from our predecessors, Nan van Geloven, Marijtje van Duijn, and Miroslav Ristic. We have immediately moved to a new format, of which we have informed you in the previous issue of Statistica Neerlandica, consisting of a fast-turnaround system with the aim of going from first submission to actual publication in two (!) months' time. Despite the efforts required on the part of the editors, associate editors and the publisher Wiley, the system seems to be working as intended. After the first half year, we are seeing the first fruits of this new approach. The first publications of the new regime are already available online, well within the 2-month target, and the number of quality submissions to Statistica Neerlandica is up. Clearly, we need to see how the system will develop in the future, but the first signs are encouraging. Besides the fast-turnaround system, we also want to diversify our offerings in the journal to better connect to the statistical society and the readers of Statistica Neerlandica. For eight decades we have only had the research paper, in which statistical researchers presented their research in a typical 20-page (or so) format. This trusted article type will obviously stay, as it a universal scientific currency with value for researchers and readers alike. From now on, however, we will also accept three new article types, in particular, Short Notes, Tutorials and State-of-the-Art reviews. Short Notes are short contributions that present a single, original, and significant discovery for rapid dissemination. They are aimed at informing colleagues about a finding, useful for the application, computation, methodology or theory of statistics. They should not be longer than 6–7 pages (2,500 words). These short notes can avoid long introductions or conclusions, and they do not need a lot of contextualization. They are little statistical gems, nice insights, useful mathematical tools that can aid the rest of the statistical community. Tutorials are aimed at introducing a general area of statistical theory, statistical methodology, statistical computing, statistical software, or an important application area of statistics. The tutorial should act as an introduction to those not already familiar with the area, and as a review to others. The mathematical level of each depends upon the topic. In all cases, however, the tutorial will strive for the broadest possible audience of researchers who comprise the readership of Statistica Neerlandica. Whereas tutorials are introductory, State-of-the-Art reviews focus on the latest developments. State-of-the-Art reviews aim at bringing an interested statistical audience up-to-date in an important and topical subject in the field of statistics with a focus on summarizing the latest advances. Although they present advanced material, th
2023年5月,一个由Edwin van den Heuvel, Veronica Vinciotti和我,Ernst Wit组成的新编辑团队,目前在Casper Albers的帮助下,接替了我们的前任Nan van Geloven, Marijtje van Duijn和Miroslav Ristic。我们已经立即移动到一个新的格式,其中我们已经通知你在前一个问题的统计荷兰,包括一个快速周转系统,从第一次提交到实际出版的目的在两个(!)个月的时间。尽管编辑、副编辑和出版商Wiley需要付出努力,但这个系统似乎正在按计划工作。上半年过去了,我们看到了这种新方法的初步成果。新制度的第一批出版物已经在网上发布,远远超过了2个月的目标,向荷兰统计局提交的高质量报告数量也在增加。显然,我们需要观察这个系统未来将如何发展,但最初的迹象令人鼓舞。除了快速周转系统,我们还希望使我们在期刊上的产品多样化,以便更好地与统计学会和《荷兰统计》的读者建立联系。80年来,我们只有研究论文,其中统计研究人员以典型的20页(左右)格式展示他们的研究。这种值得信赖的文章类型显然会继续存在,因为它是一种普遍的科学货币,对研究人员和读者都有价值。但是,从现在开始,我们还将接受3种新的文章类型,特别是Short Notes, tutorial和state -of-the- review。短文是一篇简短的文章,它提出了一个单一的、原创的、重要的发现,以便迅速传播。它们的目的是通知同事一个对应用、计算、方法或统计学理论有用的发现。简历不应超过6-7页(2500字)。这些简短的笔记可以避免冗长的介绍或结论,也不需要大量的语境化。它们是小小的统计瑰宝,有很好的见解,有用的数学工具,可以帮助统计社区的其他人。教程旨在介绍统计理论、统计方法、统计计算、统计软件或统计的重要应用领域的一般领域。对于那些不熟悉该领域的人来说,教程应该是一个介绍,同时也是对其他人的一种回顾。每个人的数学水平取决于主题。然而,在所有情况下,本教程都将争取尽可能广泛的研究人员读者,这些研究人员包括《荷兰统计》的读者。教程是介绍性的,而最新的评论则侧重于最新的发展。最新的评论旨在使有兴趣的统计读者了解统计领域中一个重要和热门主题的最新情况,重点是总结最新进展。虽然它们提供了先进的材料,但它们应该是专门和感兴趣的统计学家,而不仅仅是专家可以访问的。它们应该为感兴趣的研究人员提供一种方法,使他们能够迅速掌握某一统计主题的最新技术。因此,最先进的文章应该限制在大约12-13页(5000字)。在我们努力使《荷兰统计》再次成为Q1期刊的过程中,我们邀请社区向我们提供建议,向我们反馈我们的工作情况,当然,还请向期刊提交手稿,可以是研究论文,也可以是三种新格式之一:简短说明、教程或最新评论。我们期待着收到更多高质量的提交。
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引用次数: 0
Editorial statistics 编辑数据
3区 数学 Q2 STATISTICS & PROBABILITY Pub Date : 2023-10-17 DOI: 10.1111/stan.12325
Edwin van den Heuvel, Veronica Vinciotti, Ernst‐Jan Camiel Wit
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引用次数: 0
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Statistica Neerlandica
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