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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 1 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, Michael Kohler","doi":"10.1007/s10463-024-00898-6","DOIUrl":"https://doi.org/10.1007/s10463-024-00898-6","url":null,"abstract":"<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>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"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 1 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, Bojana Milošević","doi":"10.1007/s10463-024-00902-z","DOIUrl":"https://doi.org/10.1007/s10463-024-00902-z","url":null,"abstract":"<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>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"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 1 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, Mouna Kassa, Julien Papaïx, Kiên Kiêu, Radu S. Stoica","doi":"10.1007/s10463-023-00893-3","DOIUrl":"https://doi.org/10.1007/s10463-023-00893-3","url":null,"abstract":"<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>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"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 1 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, M. Singull
{"title":"Using the growth curve model in classification of repeated measurements","authors":"Dietrich von Rosen, M. Singull","doi":"10.1007/s10463-024-00900-1","DOIUrl":"https://doi.org/10.1007/s10463-024-00900-1","url":null,"abstract":"","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"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 1 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, Jiang Hu","doi":"10.1007/s10463-024-00896-8","DOIUrl":"https://doi.org/10.1007/s10463-024-00896-8","url":null,"abstract":"<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>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"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 1 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, Kerstin Reckruehm","doi":"10.1007/s10463-023-00892-4","DOIUrl":"https://doi.org/10.1007/s10463-023-00892-4","url":null,"abstract":"<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>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"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 1 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, Markus Pauly, Somesh Kumar","doi":"10.1007/s10463-024-00897-7","DOIUrl":"https://doi.org/10.1007/s10463-024-00897-7","url":null,"abstract":"<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>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"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
Regularized nonlinear regression with dependent errors and its application to a biomechanical model 有依赖误差的正则化非线性回归及其在生物力学模型中的应用
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-02-08 DOI: 10.1007/s10463-023-00895-1
Hojun You, Kyubaek Yoon, Wei-Ying Wu, Jongeun Choi, Chae Young Lim
{"title":"Regularized nonlinear regression with dependent errors and its application to a biomechanical model","authors":"Hojun You, Kyubaek Yoon, Wei-Ying Wu, Jongeun Choi, Chae Young Lim","doi":"10.1007/s10463-023-00895-1","DOIUrl":"https://doi.org/10.1007/s10463-023-00895-1","url":null,"abstract":"<p>A biomechanical model often requires parameter estimation and selection in a known but complicated nonlinear function. Motivated by observing that the data from a head-neck position tracking system, one of biomechanical models, show multiplicative time-dependent errors, we develop a modified penalized weighted least squares estimator. The proposed method can be also applied to a model with possible non-zero mean time-dependent additive errors. Asymptotic properties of the proposed estimator are investigated under mild conditions on a weight matrix and the error process. A simulation study demonstrates that the proposed estimation works well in both parameter estimation and selection with time-dependent error. The analysis and comparison with an existing method for head-neck position tracking data show better performance of the proposed method in terms of the variance accounted for.</p>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139753353","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
Multivariate Hawkes processes with spatial covariates for spatiotemporal event data analysis 带有空间协变量的多变量霍克斯过程，用于时空事件数据分析
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-01-29 DOI: 10.1007/s10463-023-00894-2
Chenlong Li, Kaiyan Cui
{"title":"Multivariate Hawkes processes with spatial covariates for spatiotemporal event data analysis","authors":"Chenlong Li, Kaiyan Cui","doi":"10.1007/s10463-023-00894-2","DOIUrl":"https://doi.org/10.1007/s10463-023-00894-2","url":null,"abstract":"<p>Spatiotemporal events occur in many disciplines, including economics, sociology, criminology, and seismology, with different patterns in space and time related to environmental characteristics, policing, and human behavior. In this paper, we propose a class of multivariate Hawkes processes with spatial covariates to consider the influence structure of spatial features in spatiotemporal events and the spatiotemporal patterns such as clustering. Baseline intensities are assumed to be a spatial Poisson regression model to explain spatial feature influence. The transfer functions are considered unknown but smooth and decreasing to explain the clustering phenomena. A semiparametric estimation method based on time discretization and local constant approximation is introduced. Transfer function estimators are shown to be consistent, and baseline intensity estimators are consistent and asymptotically normal. We examine the numerical performance of the proposed estimators with extensive simulation and illustrate the application of the proposed model to crime data obtained from Pittsburgh, Pennsylvania.</p>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139587932","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
Gradual change-point analysis based on Spearman matrices for multivariate time series 基于斯皮尔曼矩阵的多变量时间序列渐变点分析
IF 1 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2024-01-05 DOI: 10.1007/s10463-023-00891-5
Jean-François Quessy
{"title":"Gradual change-point analysis based on Spearman matrices for multivariate time series","authors":"Jean-François Quessy","doi":"10.1007/s10463-023-00891-5","DOIUrl":"https://doi.org/10.1007/s10463-023-00891-5","url":null,"abstract":"<p>It may happen that the behavior of a multivariate time series is such that the underlying joint distribution is gradually moving from one distribution to another between unknown times of change. Under this context of a possible gradual-change, tests of change-point detection in the dependence structure of multivariate series are developed around the associated sequence of Spearman matrices. It is formally established that the proposed test statistics for that purpose are asymptotically marginal-free under a general strong-mixing assumption, and written as functions of integrated Brownian bridges. Consistent estimators of the pair of times of change, as well as of the before-the-change and after-the-change Spearman matrices, are also proposed. A simulation study examines the sampling properties of the introduced tools, and the methodologies are illustrated on a synthetic dataset.</p>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139374266","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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