Statistics and Its Interface最新文献_第3页

Model-based statistical depth for matrix data 基于模型的矩阵数据统计深度

IF 0.8 4区数学

Statistics and Its Interface Pub Date : 2024-02-01 DOI: 10.4310/23-sii829

Yue Mu, Guanyu Hu, Wei Wu

{"title":"Model-based statistical depth for matrix data","authors":"Yue Mu, Guanyu Hu, Wei Wu","doi":"10.4310/23-sii829","DOIUrl":"https://doi.org/10.4310/23-sii829","url":null,"abstract":"The field of matrix data learning has witnessed significant advancements in recent years, encompassing diverse datasets such as medical images, social networks, and personalized recommendation systems. These advancements have found widespread application in various domains, including medicine, biology, public health, engineering, finance, economics, sports analytics, and environmental sciences. While extensive research has been conducted on estimation, inference, prediction, and computation for matrix data, the ranking problem has not received adequate attention. Statistical depth, a measure providing a centeroutward rank for different data types, has been introduced in the past few decades. However, its exploration has been limited due to the complexity of the second and higher orderstatistics. In this paper, we propose an approach to rank matrix data by employing a model-based depth framework. Our methodology involves estimating the eigen-decomposition of a 4th-order covariance tensor. To enable this process using conventional matrix operations, we specify the tensor product operator between matrices and 4th-order tensors. Furthermore, we introduce a Kronecker product form on the covariance to enhance the robustness and efficiency of the estimation process, effectively reducing the number of parameters in the model. Based on this new framework, we develop an efficient algorithm to estimate the model-based statistical depth. To validate the effectiveness of our proposed method, we conduct simulations and apply it to two real-world applications: field goal attempts of NBA players and global temperature anomalies.","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":"281 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139658971","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

Rank-R matrix autoregressive models for modeling spatio-temporal data 用于时空数据建模的 Rank-R 矩阵自回归模型

IF 0.8 4区数学

Statistics and Its Interface Pub Date : 2024-02-01 DOI: 10.4310/23-sii812

Nan-Jung Hsu, Hsin-Cheng Huang, Ruey S. Tsay, Tzu-Chieh Kao

{"title":"Rank-R matrix autoregressive models for modeling spatio-temporal data","authors":"Nan-Jung Hsu, Hsin-Cheng Huang, Ruey S. Tsay, Tzu-Chieh Kao","doi":"10.4310/23-sii812","DOIUrl":"https://doi.org/10.4310/23-sii812","url":null,"abstract":"We develop a matrix-variate autoregressive (MAR) model to analyze spatio-temporal data organized on a regular grid in space. The model is an extension of the bilinear MAR spatial model of Hsu, Huang and Tsay $href{ https://doi.org/10.1080/10618600.2021.1938587 }{[10]}$ by increasing its flexibility and applicability in empirical applications. Specifically, we propose to model each autoregressive (AR) coefficient matrix of the MAR model by $R$ bilinear terms, thereby establishing a rank‑R model. The extension can be interpreted as decomposing the AR dynamics of the data into $R$ bilinear MAR components. We further incorporate a banded neighborhood structure for AR coefficient matrices and utilize a flexible nonstationary low-rank covariance model for the spatial innovation process, leading to a parsimonious model without sacrificing its flexibility. We estimate all parameters of the model by the maximum likelihood method and develop a computationally efficient alternating direction method of multipliers algorithm, involving only closed-form expressions in all steps. Applications to a wind-speed dataset and an employment dataset, as well as two simulation experiments, demonstrate the effectiveness of the proposed method in estimation, model selection, and prediction.","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":"36 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139659193","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

Imaging mediation analysis for longitudinal outcomes: a case study of childhood brain tumor survivorship. 纵向结果的影像中介分析：儿童脑肿瘤存活个案研究。

IF 0.7 4区数学

Statistics and Its Interface Pub Date : 2024-01-01 Epub Date: 2024-07-19 DOI: 10.4310/23-sii815

Yimei Li, Jade Xiaoqing Wang, Grace Chen Zhou, Heather M Conklin, Arzu Onar-Thomas, Amar Gajjar, Wilburn E Reddick, Cai Li

{"title":"Imaging mediation analysis for longitudinal outcomes: a case study of childhood brain tumor survivorship.","authors":"Yimei Li, Jade Xiaoqing Wang, Grace Chen Zhou, Heather M Conklin, Arzu Onar-Thomas, Amar Gajjar, Wilburn E Reddick, Cai Li","doi":"10.4310/23-sii815","DOIUrl":"10.4310/23-sii815","url":null,"abstract":"<p><p>Aggressive cancer treatments that affect the central nervous system are associated with an increased risk of cognitive deficits. As treatment for pediatric brain tumors has become more effective, there has been a heightened focus on improving cognitive outcomes, which can significantly affect the quality of life for pediatric cancer survivors. This paper is motivated by and applied to a clinical trial for medulloblastoma, the most common malignant brain tumor in children. The trial collects comprehensive data including treatment-related clinical information, neuroimaging, and longitudinal neurocognitive outcomes to enhance our understanding of the responses to treatment and the enduring impacts of radiation therapy on the survivors of medulloblastoma. To this end, we have developed a new mediation model tailored for longitudinal outcomes with high-dimensional imaging mediators. Specifically, we adopt a joint binary Ising-Gaussian Markov random field prior distribution to account for spatial dependency and smoothness of ultra-high-dimensional neuroimaging mediators for enhancing detection power of informative voxels. By exploiting the proposed approach, we identify causal pathways and the corresponding white matter microstructures mediating the negative impact of irradiation on neurodevelopment. The results provide guidance on sparing the brain regions and improving long-term neurodevelopment for pediatric cancer survivors. Simulation studies also confirm the validity of the proposed method.</p>","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":"17 3","pages":"533-548"},"PeriodicalIF":0.7,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12467661/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145187440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Latent class proportional hazards regression with heterogeneous survival data 潜在类别比例风险回归与异质生存数据

IF 0.8 4区数学

Statistics and Its Interface Pub Date : 2023-11-27 DOI: 10.4310/23-sii785

Teng Fei, John J. Hanfelt, Limin Peng

引用次数: 0

Frequentist Bayesian compound inference 频率贝叶斯复合推理

IF 0.8 4区数学

Statistics and Its Interface Pub Date : 2023-11-27 DOI: 10.4310/23-sii797

Jinfeng Xu, Ao Yuan

引用次数: 0

Guiding light: An essay for Professor Lincheng Zhao on the occasion of his 80th birthday 指路明灯:赵林成教授八十大寿随笔