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Assessing the coverage probabilities of fixed-margin confidence intervals for the tail conditional allocation 评估尾部条件分配的固定边际置信区间的覆盖概率
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-04-23 DOI: 10.1007/s10463-024-00904-x
N. V. Gribkova, J. Su, R. Zitikis
{"title":"Assessing the coverage probabilities of fixed-margin confidence intervals for the tail conditional allocation","authors":"N. V. Gribkova,&nbsp;J. Su,&nbsp;R. Zitikis","doi":"10.1007/s10463-024-00904-x","DOIUrl":"10.1007/s10463-024-00904-x","url":null,"abstract":"<div><p>The tail conditional allocation plays an important role in a number of areas, including economics, finance, insurance, and management. Fixed-margin confidence intervals and the assessment of their coverage probabilities are of much interest. In this paper, we offer a convenient way to achieve these goals via resampling. The theoretical part of the paper, which is technically demanding, is rigorously established under minimal conditions to facilitate the widest practical use. A simulation-based study and an analysis of real data illustrate the performance of the developed methodology.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"76 5","pages":"821 - 850"},"PeriodicalIF":0.8,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasi-maximum likelihood estimation and penalized estimation under non-standard conditions 非标准条件下的准极大似然估计和惩罚性估计
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-04-23 DOI: 10.1007/s10463-024-00901-0
Junichiro Yoshida, Nakahiro Yoshida
{"title":"Quasi-maximum likelihood estimation and penalized estimation under non-standard conditions","authors":"Junichiro Yoshida,&nbsp;Nakahiro Yoshida","doi":"10.1007/s10463-024-00901-0","DOIUrl":"10.1007/s10463-024-00901-0","url":null,"abstract":"<div><p>The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the parameter space or where even identifiability fails. For that, we propose a more general local approximation of the parameter space (at the true value) than previous studies. This estimation theory is comprehensive in that it can handle penalized estimation as well as quasi-maximum likelihood estimation (in the ergodic or non-ergodic statistics) under such non-regular models. In penalized estimation, depending on the boundary constraint, even the concave Bridge estimator does not necessarily give selection consistency. Therefore, we describe some sufficient condition for selection consistency, precisely evaluating the balance between the boundary constraint and the form of the penalty. An example is penalized MLE of variance components of random effects in linear mixed models.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"76 5","pages":"711 - 763"},"PeriodicalIF":0.8,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A delineation of new classes of exponential dispersion models supported on the set of nonnegative integers 非负整数集支持的指数离散模型新类别划分
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-04-22 DOI: 10.1007/s10463-024-00903-y
Shaul K. Bar-Lev, Gérard Letac, Ad Ridder
{"title":"A delineation of new classes of exponential dispersion models supported on the set of nonnegative integers","authors":"Shaul K. Bar-Lev,&nbsp;Gérard Letac,&nbsp;Ad Ridder","doi":"10.1007/s10463-024-00903-y","DOIUrl":"10.1007/s10463-024-00903-y","url":null,"abstract":"<div><p>The aim of this paper is to delineate a set of new classes of natural exponential families and their associated exponential dispersion models whose probability distributions are supported on the set of nonnegative integers with positive mass on 0 and 1. The new classes are obtained by considering a specific form of their variance functions. We show that the distributions of all these classes are supported on nonnegative integers, that they are infinitely divisible, and that they are skewed to the right, leptokurtic, over-dispersed, and zero-inflated (relative to the Poisson class). Accordingly, these new classes significantly enrich the set of probability models for modeling zero-inflated and over-dispersed count data. Furthermore, we elaborate on numerical techniques how to compute the distributions of our classes, and apply these to an actual data experiment.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"76 4","pages":"679 - 709"},"PeriodicalIF":0.8,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140673175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the universal consistency of an over-parametrized deep neural network estimate learned by gradient descent 论梯度下降法学习的过参数化深度神经网络估计的普遍一致性
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-04-08 DOI: 10.1007/s10463-024-00898-6
Selina Drews, Michael Kohler
{"title":"On the universal consistency of an over-parametrized deep neural network estimate learned by gradient descent","authors":"Selina Drews,&nbsp;Michael Kohler","doi":"10.1007/s10463-024-00898-6","DOIUrl":"10.1007/s10463-024-00898-6","url":null,"abstract":"<div><p>Estimation of a multivariate regression function from independent and identically distributed data is considered. An estimate is defined which fits a deep neural network consisting of a large number of fully connected neural networks, which are computed in parallel, via gradient descent to the data. The estimate is over-parametrized in the sense that the number of its parameters is much larger than the sample size. It is shown that with a suitable random initialization of the network, a sufficiently small gradient descent step size, and a number of gradient descent steps that slightly exceed the reciprocal of this step size, the estimate is universally consistent. This means that the expected <span>(L_2)</span> error converges to zero for all distributions of the data where the response variable is square integrable.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"76 3","pages":"361 - 391"},"PeriodicalIF":0.8,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A novel two-sample test within the space of symmetric positive definite matrix distributions and its application in finance 对称正定矩阵分布空间内的新型双样本检验及其在金融领域的应用
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-04-08 DOI: 10.1007/s10463-024-00902-z
Žikica Lukić, Bojana Milošević
{"title":"A novel two-sample test within the space of symmetric positive definite matrix distributions and its application in finance","authors":"Žikica Lukić,&nbsp;Bojana Milošević","doi":"10.1007/s10463-024-00902-z","DOIUrl":"10.1007/s10463-024-00902-z","url":null,"abstract":"<div><p>This paper introduces a novel two-sample test for a broad class of orthogonally invariant positive definite symmetric matrix distributions. Our test is the first of its kind, and we derive its asymptotic distribution. To estimate the test power, we use a warp-speed bootstrap method and consider the most common matrix distributions. We provide several real data examples, including the data for main cryptocurrencies and stock data of major US companies. The real data examples demonstrate the applicability of our test in the context closely related to algorithmic trading. The popularity of matrix distributions in many applications and the need for such a test in the literature are reconciled by our findings.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"76 5","pages":"797 - 820"},"PeriodicalIF":0.8,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Statistical inference for random T-tessellations models. Application to agricultural landscape modeling 随机 T 型网格模型的统计推断。在农业景观建模中的应用
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-04-05 DOI: 10.1007/s10463-023-00893-3
Katarzyna Adamczyk-Chauvat, Mouna Kassa, Julien Papaïx, Kiên Kiêu, Radu S. Stoica
{"title":"Statistical inference for random T-tessellations models. Application to agricultural landscape modeling","authors":"Katarzyna Adamczyk-Chauvat,&nbsp;Mouna Kassa,&nbsp;Julien Papaïx,&nbsp;Kiên Kiêu,&nbsp;Radu S. Stoica","doi":"10.1007/s10463-023-00893-3","DOIUrl":"10.1007/s10463-023-00893-3","url":null,"abstract":"<div><p>The Gibbsian T-tessellation models allow the representation of a wide range of spatial patterns. This paper proposes an integrated approach for statistical inference. Model parameters are estimated via Monte Carlo maximum likelihood. The simulations needed for likelihood computation are produced using an adapted Metropolis-Hastings-Green dynamics. In order to reduce the computational costs, a pseudolikelihood estimate is derived and then used for the initialization of the likelihood optimization. Model assessment is based on global envelope tests applied to the set of functional statistics of tessellation. Finally, a real data application is presented. This application analyzes three French agricultural landscapes. The Gibbs T-tessellation models simultaneously provide a morphological and statistical characterization of these data.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"76 3","pages":"447 - 479"},"PeriodicalIF":0.8,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140565954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Using the growth curve model in classification of repeated measurements 在重复测量分类中使用生长曲线模型
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-03-29 DOI: 10.1007/s10463-024-00900-1
Dietrich von Rosen, Martin Singull
{"title":"Using the growth curve model in classification of repeated measurements","authors":"Dietrich von Rosen,&nbsp;Martin Singull","doi":"10.1007/s10463-024-00900-1","DOIUrl":"10.1007/s10463-024-00900-1","url":null,"abstract":"<div><p>In this paper, discrimination between two populations following the growth curve model is considered. A likelihood-based classification procedure is established, in the sense that we compare the two likelihoods given that the new observation belongs to respective population. The possibility to classify the new observation as belonging to an unknown population is discussed, which is shown to be natural when considering growth curves. Several examples and simulations are given to emphasize this possibility.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"76 3","pages":"511 - 534"},"PeriodicalIF":0.8,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140367528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multi-sample hypothesis testing of high-dimensional mean vectors under covariance heterogeneity 协方差异质性下高维均值向量的多样本假设检验
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-03-22 DOI: 10.1007/s10463-024-00896-8
Lixiu Wu, Jiang Hu
{"title":"Multi-sample hypothesis testing of high-dimensional mean vectors under covariance heterogeneity","authors":"Lixiu Wu,&nbsp;Jiang Hu","doi":"10.1007/s10463-024-00896-8","DOIUrl":"10.1007/s10463-024-00896-8","url":null,"abstract":"<div><p>In this paper, we focus on the hypothesis testing problem of the mean vectors of high-dimensional data in the multi-sample case. We propose two maximum-type statistics and apply a parametric bootstrap technique to compute the critical values. Unlike previous hypothesis testing methods that heavily depend on the structural assumptions of the unknown covariance matrix, the proposed methods accommodate a general covariance structure. Additionally, we introduce screening-based testing procedures to enhance the power of our tests. These test procedures do not require the use of approximate limiting distributions for the test statistics. Finally, we obtain and verify the theoretical properties through simulation studies.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"76 4","pages":"579 - 615"},"PeriodicalIF":0.8,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140204420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Data segmentation for time series based on a general moving sum approach 基于一般移动总和方法的时间序列数据分割
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-03-14 DOI: 10.1007/s10463-023-00892-4
Claudia Kirch, Kerstin Reckruehm
{"title":"Data segmentation for time series based on a general moving sum approach","authors":"Claudia Kirch,&nbsp;Kerstin Reckruehm","doi":"10.1007/s10463-023-00892-4","DOIUrl":"10.1007/s10463-023-00892-4","url":null,"abstract":"<div><p>We consider the multiple change point problem in a general framework based on estimating equations. This extends classical sample mean-based methodology to include robust methods but also different types of changes such as changes in linear regression or changes in count data including Poisson autoregressive time series. In this framework, we derive a general theory proving consistency for the number of change points and rates of convergence for the estimators of the locations of the change points. More precisely, two different types of MOSUM (moving sum) statistics are considered: A MOSUM-Wald statistic based on differences of local estimators and a MOSUM-score statistic based on a global inspection parameter. The latter is usually computationally less involved in particular in nonlinear problems where no closed form of the estimator is known such that numerical methods are required. Finally, we evaluate the methodology by some simulations as well as using geophysical well-log data.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"76 3","pages":"393 - 421"},"PeriodicalIF":0.8,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Testing against ordered alternatives in one-way ANOVA model with exponential errors 在指数误差的单向方差分析模型中对有序备选方案进行测试
IF 0.8 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-03-12 DOI: 10.1007/s10463-024-00897-7
Anjana Mondal, Markus Pauly, Somesh Kumar
{"title":"Testing against ordered alternatives in one-way ANOVA model with exponential errors","authors":"Anjana Mondal,&nbsp;Markus Pauly,&nbsp;Somesh Kumar","doi":"10.1007/s10463-024-00897-7","DOIUrl":"10.1007/s10463-024-00897-7","url":null,"abstract":"<div><p>In this paper, a one-way heteroscedastic ANOVA model is considered with exponentially distributed errors. The likelihood ratio test (LRT) and two multiple comparison tests are developed for testing against ordered alternatives. A parametric bootstrap (PB) approach is proposed for implementation of tests and its asymptotic accuracy is proved. An extensive simulation study shows that all the proposed tests are accurate in terms of achieving the nominal size value, even for small samples. The proposed simultaneous confidence intervals are also seen to maintain the preassigned coverage probability. The powers of these tests are compared with a recently proposed test, which is quite conservative. Finally, the proposed tests are illustrated with the help of three data sets related to medical studies. We have developed an ‘R’ package for implementing our test procedures and shared it on the open platform ‘GitHub.’</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"76 4","pages":"649 - 678"},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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