{"title":"具有测量误差的高维向量自回归的统计推断","authors":"Xiang Lyu, Jian Kang, Lexin Li","doi":"10.5705/ss.202021.0151","DOIUrl":null,"url":null,"abstract":"<p><p>High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model. While there has been a large body of literature studying sparse estimation of the transition matrix, there is a paucity of inference solutions, especially in the high-dimensional scenario. We develop inferential procedures for both the global and simultaneous testing of the transition matrix. We first develop a new sparse expectation-maximization algorithm to estimate the model parameters, and carefully characterize their estimation precisions. We then construct a Gaussian matrix, after proper bias and variance corrections, from which we derive the test statistics. Finally, we develop the testing procedures and establish their asymptotic guarantees. We study the finite-sample performance of our tests through intensive simulations, and illustrate with a brain connectivity analysis example.</p>","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":" ","pages":"1435-1459"},"PeriodicalIF":1.5000,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11623288/pdf/","citationCount":"0","resultStr":"{\"title\":\"Statistical Inference for High-Dimensional Vector Autoregression with Measurement Error.\",\"authors\":\"Xiang Lyu, Jian Kang, Lexin Li\",\"doi\":\"10.5705/ss.202021.0151\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model. While there has been a large body of literature studying sparse estimation of the transition matrix, there is a paucity of inference solutions, especially in the high-dimensional scenario. We develop inferential procedures for both the global and simultaneous testing of the transition matrix. We first develop a new sparse expectation-maximization algorithm to estimate the model parameters, and carefully characterize their estimation precisions. We then construct a Gaussian matrix, after proper bias and variance corrections, from which we derive the test statistics. Finally, we develop the testing procedures and establish their asymptotic guarantees. We study the finite-sample performance of our tests through intensive simulations, and illustrate with a brain connectivity analysis example.</p>\",\"PeriodicalId\":49478,\"journal\":{\"name\":\"Statistica Sinica\",\"volume\":\" \",\"pages\":\"1435-1459\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2023-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11623288/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistica Sinica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5705/ss.202021.0151\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistica Sinica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5705/ss.202021.0151","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Statistical Inference for High-Dimensional Vector Autoregression with Measurement Error.
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model. While there has been a large body of literature studying sparse estimation of the transition matrix, there is a paucity of inference solutions, especially in the high-dimensional scenario. We develop inferential procedures for both the global and simultaneous testing of the transition matrix. We first develop a new sparse expectation-maximization algorithm to estimate the model parameters, and carefully characterize their estimation precisions. We then construct a Gaussian matrix, after proper bias and variance corrections, from which we derive the test statistics. Finally, we develop the testing procedures and establish their asymptotic guarantees. We study the finite-sample performance of our tests through intensive simulations, and illustrate with a brain connectivity analysis example.
期刊介绍:
Statistica Sinica aims to meet the needs of statisticians in a rapidly changing world. It provides a forum for the publication of innovative work of high quality in all areas of statistics, including theory, methodology and applications. The journal encourages the development and principled use of statistical methodology that is relevant for society, science and technology.