Statistical modeling for massive spatial data sets has generated a substantial literature on scalable spatial processes based upon Vecchia's approximation. Vecchia's approximation for Gaussian process models enables fast evaluation of the likelihood by restricting dependencies at a location to its neighbors. We establish inferential properties of microergodic spatial covariance parameters within the paradigm of fixed-domain asymptotics when they are estimated using Vecchia's approximation. The conditions required to formally establish these properties are explored, theoretically and empirically, and the effectiveness of Vecchia's approximation is further corroborated from the standpoint of fixed-domain asymptotics.
{"title":"Fixed-Domain Asymptotics Under Vecchia's Approximation of Spatial Process Likelihoods.","authors":"Lu Zhang, Wenpin Tang, Sudipto Banerjee","doi":"10.5705/ss.202021.0428","DOIUrl":"10.5705/ss.202021.0428","url":null,"abstract":"<p><p>Statistical modeling for massive spatial data sets has generated a substantial literature on scalable spatial processes based upon Vecchia's approximation. Vecchia's approximation for Gaussian process models enables fast evaluation of the likelihood by restricting dependencies at a location to its neighbors. We establish inferential properties of microergodic spatial covariance parameters within the paradigm of fixed-domain asymptotics when they are estimated using Vecchia's approximation. The conditions required to formally establish these properties are explored, theoretically and empirically, and the effectiveness of Vecchia's approximation is further corroborated from the standpoint of fixed-domain asymptotics.</p>","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11444644/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42635545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Multi-modal data are prevalent in many scientific fields. In this study, we consider the parameter estimation and variable selection for a multi-response regression using block-missing multi-modal data. Our method allows the dimensions of both the responses and the predictors to be large, and the responses to be incomplete and correlated, a common practical problem in high-dimensional settings. Our proposed method uses two steps to make a prediction from a multi-response linear regression model with block-missing multi-modal predictors. In the first step, without imputing missing data, we use all available data to estimate the covariance matrix of the predictors and the cross-covariance matrix between the predictors and the responses. In the second step, we use these matrices and a penalized method to simultaneously estimate the precision matrix of the response vector, given the predictors, and the sparse regression parameter matrix. Lastly, we demonstrate the effectiveness of the proposed method using theoretical studies, simulated examples, and an analysis of a multi-modal imaging data set from the Alzheimer's Disease Neuroimaging Initiative.
{"title":"Multi-response Regression for Block-missing Multi-modal Data without Imputation.","authors":"Haodong Wang, Quefeng Li, Yufeng Liu","doi":"10.5705/ss.202021.0170","DOIUrl":"10.5705/ss.202021.0170","url":null,"abstract":"<p><p>Multi-modal data are prevalent in many scientific fields. In this study, we consider the parameter estimation and variable selection for a multi-response regression using block-missing multi-modal data. Our method allows the dimensions of both the responses and the predictors to be large, and the responses to be incomplete and correlated, a common practical problem in high-dimensional settings. Our proposed method uses two steps to make a prediction from a multi-response linear regression model with block-missing multi-modal predictors. In the first step, without imputing missing data, we use all available data to estimate the covariance matrix of the predictors and the cross-covariance matrix between the predictors and the responses. In the second step, we use these matrices and a penalized method to simultaneously estimate the precision matrix of the response vector, given the predictors, and the sparse regression parameter matrix. Lastly, we demonstrate the effectiveness of the proposed method using theoretical studies, simulated examples, and an analysis of a multi-modal imaging data set from the Alzheimer's Disease Neuroimaging Initiative.</p>","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11035992/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70937715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonparametric Estimation and Testing for Panel Count Data with Informative Terminal Event","authors":"Xiangbin Hu, Li Liu, Ying Zhang, Xingqiu Zhao","doi":"10.5705/ss.202021.0213","DOIUrl":"https://doi.org/10.5705/ss.202021.0213","url":null,"abstract":"","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70937423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: In this paper, we investigate impact analysis and its asymptotic inference for spatial autoregressive models. LeSage and Pace (2009) introduce impact analysis for spatial models and use Monte Carlo simulations to compute the dispersion. We propose to use the delta method, which enables us to obtain the dispersion in an explicit form. In addition, we provide the element-wise impact analysis. We first study the cross-sectional case, where various impacts are introduced to measure the interaction and feedback effects in a space dimension. We then study the spatial dynamic panel case with simultaneous spatial and dynamic feedback involved in the impacts. Monte Carlo results show that the proposed impact analysis has satisfactory finite sample properties. Finally, we apply impact analysis to investigate how meteorological factors and air pollutants affect PM 2 . 5 in Chinese cities.
{"title":"Impact Analysis for Spatial Autoregressive Models: With Application to Air Pollution in China","authors":"Hsuan-Yu Chang, Jihai Yu","doi":"10.5705/ss.202021.0119","DOIUrl":"https://doi.org/10.5705/ss.202021.0119","url":null,"abstract":": In this paper, we investigate impact analysis and its asymptotic inference for spatial autoregressive models. LeSage and Pace (2009) introduce impact analysis for spatial models and use Monte Carlo simulations to compute the dispersion. We propose to use the delta method, which enables us to obtain the dispersion in an explicit form. In addition, we provide the element-wise impact analysis. We first study the cross-sectional case, where various impacts are introduced to measure the interaction and feedback effects in a space dimension. We then study the spatial dynamic panel case with simultaneous spatial and dynamic feedback involved in the impacts. Monte Carlo results show that the proposed impact analysis has satisfactory finite sample properties. Finally, we apply impact analysis to investigate how meteorological factors and air pollutants affect PM 2 . 5 in Chinese cities.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70937305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonlinear dimension reduction for functional data with application to clustering","authors":"Ruoxu Tan, Yiming Zang, G. Yin","doi":"10.5705/ss.202021.0393","DOIUrl":"https://doi.org/10.5705/ss.202021.0393","url":null,"abstract":"Nonlinear dimension reduction for functional data with application to clustering","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70937980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: Boosting methods have been broadly discussed for various settings, and most methods handle data with complete observations. Although some methods are available for survival data with censored responses, they tend to assume a specific model for the survival process, and most provide numerical implementation procedures without rigorous theoretical justifications. In this paper, we develop an unbiased boosting estimation method for censored survival data, without assuming an explicit model, and explore three strategies for adjusting the loss functions, while accommodating censoring effects. We implement the proposed method using a functional gradient descent algorithm, and rigorously establish our theoretical results, including the consistency and optimization convergence. Our numerical studies show that the proposed method exhibits satisfactory performance in finite-sample settings.
{"title":"Unbiased Boosting Estimation for Censored Survival Data","authors":"Li‐Pang Chen, G. Yi","doi":"10.5705/ss.202021.0050","DOIUrl":"https://doi.org/10.5705/ss.202021.0050","url":null,"abstract":": Boosting methods have been broadly discussed for various settings, and most methods handle data with complete observations. Although some methods are available for survival data with censored responses, they tend to assume a specific model for the survival process, and most provide numerical implementation procedures without rigorous theoretical justifications. In this paper, we develop an unbiased boosting estimation method for censored survival data, without assuming an explicit model, and explore three strategies for adjusting the loss functions, while accommodating censoring effects. We implement the proposed method using a functional gradient descent algorithm, and rigorously establish our theoretical results, including the consistency and optimization convergence. Our numerical studies show that the proposed method exhibits satisfactory performance in finite-sample settings.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70936904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: Discriminant analyses of multidimensional array data (i.e., tensors) are of substantial interest in numerous statistics and engineering research problems, such as signal processing, imaging, genetics, and brain–computer interfaces. In this study, we consider a multi-class discriminant analysis with a tensor-variate predictor and a categorical response. To overcome the high dimensionality and to exploit the tensor correlation structure, we propose the discriminant analysis with tensor envelope (DATE) model for simultaneous dimension reduction and classification. We extend the notion of tensor envelopes from regression to discriminant analysis and develop two complementary estimation procedures: DATE-L is a likelihood-based estimator that is shown to be asymptotically efficient when the sample size goes to infinity and the tensor dimension is fixed; DATE-D is a novel decomposition-based estimator suitable for high-dimensional problems. Interestingly, we show that DATE-D is still root-n consistent, even when the tensor dimensions on each model grow arbitrarily fast, but at a similar rate. We demonstrate the robustness and effi-ciency of our estimators using extensive simulations and real-data examples.
{"title":"Parsimonious Tensor Discriminant Analysis","authors":"Ning Wang, Wenjing Wang, Xin Zhang","doi":"10.5705/ss.202020.0496","DOIUrl":"https://doi.org/10.5705/ss.202020.0496","url":null,"abstract":": Discriminant analyses of multidimensional array data (i.e., tensors) are of substantial interest in numerous statistics and engineering research problems, such as signal processing, imaging, genetics, and brain–computer interfaces. In this study, we consider a multi-class discriminant analysis with a tensor-variate predictor and a categorical response. To overcome the high dimensionality and to exploit the tensor correlation structure, we propose the discriminant analysis with tensor envelope (DATE) model for simultaneous dimension reduction and classification. We extend the notion of tensor envelopes from regression to discriminant analysis and develop two complementary estimation procedures: DATE-L is a likelihood-based estimator that is shown to be asymptotically efficient when the sample size goes to infinity and the tensor dimension is fixed; DATE-D is a novel decomposition-based estimator suitable for high-dimensional problems. Interestingly, we show that DATE-D is still root-n consistent, even when the tensor dimensions on each model grow arbitrarily fast, but at a similar rate. We demonstrate the robustness and effi-ciency of our estimators using extensive simulations and real-data examples.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70936940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Zero-imputation Approach in Recommendation Systems with Data Missing Heterogeneously","authors":"Jiashen Lu, Kehui Chen","doi":"10.5705/ss.202021.0429","DOIUrl":"https://doi.org/10.5705/ss.202021.0429","url":null,"abstract":"","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70938173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Kernel Regression Utilizing External Information as Constraints","authors":"Chi-Shian Dai, Jun Shao","doi":"10.5705/ss.202021.0446","DOIUrl":"https://doi.org/10.5705/ss.202021.0446","url":null,"abstract":"","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70938185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ruoyu P. T. Wang, Qihua Wang, Wang Miao, Xiaohua Zhou
The supplementary
补充
{"title":"Sharp Bounds for Variance of Treatment Effect Estimators in the Presence of Covariates","authors":"Ruoyu P. T. Wang, Qihua Wang, Wang Miao, Xiaohua Zhou","doi":"10.5705/ss.202021.0351","DOIUrl":"https://doi.org/10.5705/ss.202021.0351","url":null,"abstract":"The supplementary","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70937449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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