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Pathwise least-squares estimator for linear SPDEs with additive fractional noise 具有加性分数噪声的线性SPDEs的路径最小二乘估计
IF 1.1 4区 数学
Electronic Journal of Statistics Pub Date : 2022-03-10 DOI: 10.1214/22-EJS1990
Pavel Kvr'ivz, Jana vSnup'arkov'a
{"title":"Pathwise least-squares estimator for linear SPDEs with additive fractional noise","authors":"Pavel Kvr'ivz, Jana vSnup'arkov'a","doi":"10.1214/22-EJS1990","DOIUrl":"https://doi.org/10.1214/22-EJS1990","url":null,"abstract":"This paper deals with the drift estimation in linear stochastic evolution equations (with emphasis on linear SPDEs) with additive fractional noise (with Hurst index ranging from 0 to 1) via least-squares procedure. Since the least-squares estimator contains stochastic integrals of divergence type, we address the problem of its pathwise (and robust to observation errors) evaluation by comparison with the pathwise integral of Stratonovich type and using its chain-rule property. The resulting pathwise LSE is then defined implicitly as a solution to a non-linear equation. We study its numerical properties (existence and uniqueness of the solution) as well as statistical properties (strong consistency and the speed of its convergence). The asymptotic properties are obtained assuming fixed time horizon and increasing number of the observed Fourier modes (space asymptotics). We also conjecture the asymptotic normality of the pathwise LSE.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088611","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
Deconvolution of spherical data corrupted with unknown noise 带有未知噪声的球面数据的反褶积
IF 1.1 4区 数学
Electronic Journal of Statistics Pub Date : 2022-03-01 DOI: 10.1214/23-ejs2106
J'er'emie Capitao-Miniconi, E. Gassiat
{"title":"Deconvolution of spherical data corrupted with unknown noise","authors":"J'er'emie Capitao-Miniconi, E. Gassiat","doi":"10.1214/23-ejs2106","DOIUrl":"https://doi.org/10.1214/23-ejs2106","url":null,"abstract":"We consider the deconvolution problem for densities supported on a $(d-1)$-dimensional sphere with unknown center and unknown radius, in the situation where the distribution of the noise is unknown and without any other observations. We propose estimators of the radius, of the center, and of the density of the signal on the sphere that are proved consistent without further information. The estimator of the radius is proved to have almost parametric convergence rate for any dimension $d$. When $d=2$, the estimator of the density is proved to achieve the same rate of convergence over Sobolev regularity classes of densities as when the noise distribution is known.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43791674","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: 1
Bayesian inference and prediction for mean-mixtures of normal distributions 正态分布均值混合的贝叶斯推断与预测
IF 1.1 4区 数学
Electronic Journal of Statistics Pub Date : 2022-02-01 DOI: 10.1214/23-ejs2142
Pankaj Bhagwat, É. Marchand
{"title":"Bayesian inference and prediction for mean-mixtures of normal distributions","authors":"Pankaj Bhagwat, É. Marchand","doi":"10.1214/23-ejs2142","DOIUrl":"https://doi.org/10.1214/23-ejs2142","url":null,"abstract":"We study frequentist risk properties of predictive density estimators for mean mixtures of multivariate normal distributions, involving an unknown location parameter $theta in mathbb{R}^d$, and which include multivariate skew normal distributions. We provide explicit representations for Bayesian posterior and predictive densities, including the benchmark minimum risk equivariant (MRE) density, which is minimax and generalized Bayes with respect to an improper uniform density for $theta$. For four dimensions or more, we obtain Bayesian densities that improve uniformly on the MRE density under Kullback-Leibler loss. We also provide plug-in type improvements, investigate implications for certain type of parametric restrictions on $theta$, and illustrate and comment the findings based on numerical evaluations.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43938179","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
Conditional empirical copula processes and generalized measures of association 条件经验copula过程与广义关联测度
IF 1.1 4区 数学
Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2075
A. Derumigny, J. Fermanian
{"title":"Conditional empirical copula processes and generalized measures of association","authors":"A. Derumigny, J. Fermanian","doi":"10.1214/22-ejs2075","DOIUrl":"https://doi.org/10.1214/22-ejs2075","url":null,"abstract":"","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45621509","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
Sufficient dimension reduction for survival data analysis with error-prone variables 对易出错变量的生存数据分析进行足够的降维
IF 1.1 4区 数学
Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs1977
Li‐Pang Chen, G. Yi
{"title":"Sufficient dimension reduction for survival data analysis with error-prone variables","authors":"Li‐Pang Chen, G. Yi","doi":"10.1214/22-ejs1977","DOIUrl":"https://doi.org/10.1214/22-ejs1977","url":null,"abstract":": Sufficient dimension reduction (SDR) is an important tool in regression analysis which reduces the dimension of covariates without losing predictive information. Several methods have been proposed to handle data with either censoring in the response or measurement error in covariates. However, little research is available to deal with data having these two features simultaneously. In this paper, we examine this problem. We start with considering the cumulative distribution function in regular settings and propose a valid SDR method to incorporate the effects of censored data and covariates measurement error. Theoretical results are established, and numerical studies are reported to assess the performance of the proposed methods.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43949116","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: 2
Determine the number of clusters by data augmentation 通过数据扩充确定集群的数量
IF 1.1 4区 数学
Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2032
Wei Luo
{"title":"Determine the number of clusters by data augmentation","authors":"Wei Luo","doi":"10.1214/22-ejs2032","DOIUrl":"https://doi.org/10.1214/22-ejs2032","url":null,"abstract":"","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43358941","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: 1
Augmented direct learning for conditional average treatment effect estimation with double robustness 双鲁棒条件平均处理效果估计的增强直接学习
IF 1.1 4区 数学
Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2025
Haomiao Meng, Xingye Qiao
{"title":"Augmented direct learning for conditional average treatment effect estimation with double robustness","authors":"Haomiao Meng, Xingye Qiao","doi":"10.1214/22-ejs2025","DOIUrl":"https://doi.org/10.1214/22-ejs2025","url":null,"abstract":"","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46400127","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: 1
De-noising analysis of noisy data under mixed graphical models 混合图形模型下噪声数据的去噪分析
IF 1.1 4区 数学
Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2028
Li‐Pang Chen, G. Yi
{"title":"De-noising analysis of noisy data under mixed graphical models","authors":"Li‐Pang Chen, G. Yi","doi":"10.1214/22-ejs2028","DOIUrl":"https://doi.org/10.1214/22-ejs2028","url":null,"abstract":"","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46756070","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
Robust sieve M-estimation with an application to dimensionality reduction 鲁棒筛m估计及其在降维中的应用
IF 1.1 4区 数学
Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2038
J. Bodelet, D. La Vecchia
{"title":"Robust sieve M-estimation with an application to dimensionality reduction","authors":"J. Bodelet, D. La Vecchia","doi":"10.1214/22-ejs2038","DOIUrl":"https://doi.org/10.1214/22-ejs2038","url":null,"abstract":"","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088450","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
Robust deep neural network estimation for multi-dimensional functional data 多维函数数据的鲁棒深度神经网络估计
IF 1.1 4区 数学
Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2093
Shuoyang Wang, Guanqun Cao
{"title":"Robust deep neural network estimation for multi-dimensional functional data","authors":"Shuoyang Wang, Guanqun Cao","doi":"10.1214/22-ejs2093","DOIUrl":"https://doi.org/10.1214/22-ejs2093","url":null,"abstract":": In this paper, we propose a robust estimator for the location function from multi-dimensional functional data. The proposed estimators are based on the deep neural networks with ReLU activation function. At the meanwhile, the estimators are less susceptible to outlying observations and model-misspecification. For any multi-dimensional functional data, we provide the uniform convergence rates for the proposed robust deep neural networks estimators. Simulation studies illustrate the competitive performance of the robust deep neural network estimators on regular data and their superior performance on data that contain anomalies. The proposed method is also applied to analyze 2D and 3D images of patients with Alzheimer’s disease obtained from the Alzheimer Disease Neuroimaging Initiative database.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41537501","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: 1
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