{"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}
: 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.
{"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}
{"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}
{"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}
{"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}
{"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}
: 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.
{"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}
{"title":"Depth level set estimation and associated risk measures","authors":"Sara Armaut, Roland Diel, T. Laloë","doi":"10.1214/22-ejs2095","DOIUrl":"https://doi.org/10.1214/22-ejs2095","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":"42920277","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}
Abstract: Current status censoring (CSC) implies that there is no direct access to the lifetime of an event of interest. Instead it is known if the event already occurred or not at a random monitoring time. CSC is a simple sampling procedure and in many cases the only possibility to assess the lifetime of interest. At the same time, the absence of a direct measurement of a lifetime of interest makes the problem of nonparametric distribution estimation ill-posed. A simple, adaptive and sharp minimax estimator of the density and cumulative distribution function is proposed. The simplicity of estimator also allows us to relax assumptions. Practical examples illustrate CSC problem and the proposed estimator.
{"title":"Efficient nonparametric estimation of distribution for current status censoring","authors":"S. Efromovich","doi":"10.1214/22-ejs1980","DOIUrl":"https://doi.org/10.1214/22-ejs1980","url":null,"abstract":"Abstract: Current status censoring (CSC) implies that there is no direct access to the lifetime of an event of interest. Instead it is known if the event already occurred or not at a random monitoring time. CSC is a simple sampling procedure and in many cases the only possibility to assess the lifetime of interest. At the same time, the absence of a direct measurement of a lifetime of interest makes the problem of nonparametric distribution estimation ill-posed. A simple, adaptive and sharp minimax estimator of the density and cumulative distribution function is proposed. The simplicity of estimator also allows us to relax assumptions. Practical examples illustrate CSC problem and the proposed estimator.","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":"45616109","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}
. The ideal probabilistic forecast for a random variable Y based on an information set F is the conditional distribution of Y given F . In the context of point forecasts aiming to specify a functional T such as the mean, a quantile or a risk measure, the ideal point forecast is the respective functional applied to the conditional distribution. This paper provides a theoretical justification why this ideal forecast is actually a forecast, that is, an F -measurable random variable. To that end, the appropriate notion of measurability of T is clarified and this measurability is established for a large class of practically relevant functionals, including elicitable ones. More generally, the measurability of T implies the measurability of any point forecast which arises by applying T to a probabilistic forecast. Similar measurability results are established for proper scoring rules, the main tool to evaluate the predictive accuracy of probabilistic forecasts.
{"title":"Measurability of functionals and of ideal point forecasts","authors":"Tobias Fissler, H. Holzmann","doi":"10.1214/22-EJS2062","DOIUrl":"https://doi.org/10.1214/22-EJS2062","url":null,"abstract":". The ideal probabilistic forecast for a random variable Y based on an information set F is the conditional distribution of Y given F . In the context of point forecasts aiming to specify a functional T such as the mean, a quantile or a risk measure, the ideal point forecast is the respective functional applied to the conditional distribution. This paper provides a theoretical justification why this ideal forecast is actually a forecast, that is, an F -measurable random variable. To that end, the appropriate notion of measurability of T is clarified and this measurability is established for a large class of practically relevant functionals, including elicitable ones. More generally, the measurability of T implies the measurability of any point forecast which arises by applying T to a probabilistic forecast. Similar measurability results are established for proper scoring rules, the main tool to evaluate the predictive accuracy of probabilistic forecasts.","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":"43792730","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}
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