This paper studies density estimation and regression analysis with data observed on a general unit hypersphere and contaminated by measurement errors. We establish novel density and regression estimators, and study their asymptotic properties such as the rates of convergence and asymptotic normality. We also provide two types of asymptotic confidence intervals for both density and regression functions. One type is based on the asymptotic normality of their estimators and the other type is based on the empirical likelihood technique. We present practical details on the implementation of our method as well as simulation studies and real data analysis.This article is protected by copyright. All rights reserved.
{"title":"Density estimation and regression analysis on hyperspheres in the presence of measurement error","authors":"Jeong Min Jeon, I. Van Keilegom","doi":"10.1111/sjos.12684","DOIUrl":"https://doi.org/10.1111/sjos.12684","url":null,"abstract":"This paper studies density estimation and regression analysis with data observed on a general unit hypersphere and contaminated by measurement errors. We establish novel density and regression estimators, and study their asymptotic properties such as the rates of convergence and asymptotic normality. We also provide two types of asymptotic confidence intervals for both density and regression functions. One type is based on the asymptotic normality of their estimators and the other type is based on the empirical likelihood technique. We present practical details on the implementation of our method as well as simulation studies and real data analysis.This article is protected by copyright. All rights reserved.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48268385","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}
Ge Zhao, Yanyuan Ma, Jill S Hasler, S. Damrauer, Michael G. Levin, Jinbo Chen
We propose a nested semiparametric model to analyze a case-control study where genuine case status is missing for some individuals. The concept of a noncase is introduced to allow for the imputation of the missing genuine cases. The odds ratio parameter of the genuine cases compared to controls is of interest. The imputation procedure predicts the probability of being a genuine case compared to a noncase semiparametrically in a dimen-sion reduction fashion. This procedure is flexible, and vastly generalizes the existing methods. We establish the root-n asymptotic normality of the odds ratio parameter estimator. Our method yields stable odds ratio parameter estimation owing to the application of an efficient semiparametric sufficient dimension reduction estimator. We conduct finite sample numerical simulations to illustrate the performance of our approach, and apply it to a dilated cardiomyopathy study.
{"title":"A Nested Semiparametric Method for Case‐Control Study with Missingness","authors":"Ge Zhao, Yanyuan Ma, Jill S Hasler, S. Damrauer, Michael G. Levin, Jinbo Chen","doi":"10.1111/sjos.12673","DOIUrl":"https://doi.org/10.1111/sjos.12673","url":null,"abstract":"We propose a nested semiparametric model to analyze a case-control study where genuine case status is missing for some individuals. The concept of a noncase is introduced to allow for the imputation of the missing genuine cases. The odds ratio parameter of the genuine cases compared to controls is of interest. The imputation procedure predicts the probability of being a genuine case compared to a noncase semiparametrically in a dimen-sion reduction fashion. This procedure is flexible, and vastly generalizes the existing methods. We establish the root-n asymptotic normality of the odds ratio parameter estimator. Our method yields stable odds ratio parameter estimation owing to the application of an efficient semiparametric sufficient dimension reduction estimator. We conduct finite sample numerical simulations to illustrate the performance of our approach, and apply it to a dilated cardiomyopathy study.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41394265","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}
We are interested in creating statistical methods to provide informative summaries of random fields through the geometry of their excursion sets. To this end, we introduce an estimator for the length of the perimeter of excursion sets of random fields on ℝ2 observed over regular square tilings. The proposed estimator acts on the empirically accessible binary digital images of the excursion regions and computes the length of a piecewise linear approximation of the excursion boundary. The estimator is shown to be consistent as the pixel size decreases, without the need of any normalization constant, and with neither assumption of Gaussianity nor isotropy imposed on the underlying random field. In this general framework, even when the domain grows to cover ℝ2, the estimation error is shown to be of smaller order than the side length of the domain. For affine, strongly mixing random fields, this translates to a multivariate Central Limit Theorem for our estimator when multiple levels are considered simultaneously. Finally, we conduct several numerical studies to investigate statistical properties of the proposed estimator in the finite‐sample data setting.This article is protected by copyright. All rights reserved.
{"title":"On the perimeter estimation of pixelated excursion sets of 2D anisotropic random fields","authors":"Ryan Cotsakis, Elena Di Bernardino, T. Opitz","doi":"10.1111/sjos.12682","DOIUrl":"https://doi.org/10.1111/sjos.12682","url":null,"abstract":"We are interested in creating statistical methods to provide informative summaries of random fields through the geometry of their excursion sets. To this end, we introduce an estimator for the length of the perimeter of excursion sets of random fields on ℝ2 observed over regular square tilings. The proposed estimator acts on the empirically accessible binary digital images of the excursion regions and computes the length of a piecewise linear approximation of the excursion boundary. The estimator is shown to be consistent as the pixel size decreases, without the need of any normalization constant, and with neither assumption of Gaussianity nor isotropy imposed on the underlying random field. In this general framework, even when the domain grows to cover ℝ2, the estimation error is shown to be of smaller order than the side length of the domain. For affine, strongly mixing random fields, this translates to a multivariate Central Limit Theorem for our estimator when multiple levels are considered simultaneously. Finally, we conduct several numerical studies to investigate statistical properties of the proposed estimator in the finite‐sample data setting.This article is protected by copyright. All rights reserved.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47849184","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}
Shuoyang Wang, Guanqun Cao, Zuofeng Shang, Michael W. Weiner, Paul Aisen, Ronald Petersen, Michael W. Weiner, Paul Aisen, Ronald Petersen, Clifford R. Jack, William Jagust, John Q. Trojanowki, Arthur W. Toga, Laurel Beckett, Robert C. Green, Andrew J. Saykin, John C. Morris, Richard J. Perrin, Leslie M. Shaw, Zaven Khachaturian, Maria Carrillo, William Potter, Lisa Barnes, Marie Bernard, Hector González, Carole Ho, John K. Hsiao, Jonathan Jackson, Eliezer Masliah, Donna Masterman, Ozioma Okonkwo, Richard Perrin, Laurie Ryan, Nina Silverberg, Adam Fleisher, Michael W. Weiner, Diana Truran Sacrey, Juliet Fockler, Cat Conti, Dallas Veitch, John Neuhaus, Chengshi Jin, Rachel Nosheny, Miriam Ashford, Derek Flenniken, Adrienne Kormos, Robert C. Green, Tom Montine, Cat Conti, Ronald Petersen, Paul Aisen, Michael Rafii, Rema Raman, Gustavo Jimenez, Michael Donohue, Devon Gessert, Jennifer Salazar, Caileigh Zimmerman, Yuliana Cabrera, Sarah Walter, Garrett Miller, Godfrey Coker, Taylor Clanton, Lindsey Hergesheimer, Stephanie Smith, Olusegun Adegoke, Payam Mahboubi, Shelley Moore, Jeremy Pizzola, Elizabeth Shaffer, Brittany Sloan, Laurel Beckett, Danielle Harvey, Michael Donohue, Clifford R. Jack, Arvin Forghanian‐Arani, Bret Borowski, Chad Ward, Christopher Schwarz, David Jones, Jeff Gunter, Kejal Kantarci, Matthew Senjem, Prashanthi Vemuri, Robert Reid, Nick C. Fox, Ian Malone, Paul Thompson, Sophia I. Thomopoulos, Talia M. Nir, Neda Jahanshad, Charles DeCarli, Alexander Knaack, Evan Fletcher, Danielle Harvey, Duygu Tosun‐Turgut, Stephanie Rossi Chen, Mark Choe, Karen Crawford, Paul A. Yushkevich
Abstract We propose a new approach, called as functional deep neural network (FDNN), for classifying multidimensional functional data. Specifically, a deep neural network is trained based on the principal components of the training data which shall be used to predict the class label of a future data function. Unlike the popular functional discriminant analysis approaches which only work for one‐dimensional functional data, the proposed FDNN approach applies to general non‐Gaussian multidimensional functional data. Moreover, when the log density ratio possesses a locally connected functional modular structure, we show that FDNN achieves minimax optimality. The superiority of our approach is demonstrated through both simulated and real‐world datasets.
{"title":"Deep neural network classifier for multidimensional functional data","authors":"Shuoyang Wang, Guanqun Cao, Zuofeng Shang, Michael W. Weiner, Paul Aisen, Ronald Petersen, Michael W. Weiner, Paul Aisen, Ronald Petersen, Clifford R. Jack, William Jagust, John Q. Trojanowki, Arthur W. Toga, Laurel Beckett, Robert C. Green, Andrew J. Saykin, John C. Morris, Richard J. Perrin, Leslie M. Shaw, Zaven Khachaturian, Maria Carrillo, William Potter, Lisa Barnes, Marie Bernard, Hector González, Carole Ho, John K. Hsiao, Jonathan Jackson, Eliezer Masliah, Donna Masterman, Ozioma Okonkwo, Richard Perrin, Laurie Ryan, Nina Silverberg, Adam Fleisher, Michael W. Weiner, Diana Truran Sacrey, Juliet Fockler, Cat Conti, Dallas Veitch, John Neuhaus, Chengshi Jin, Rachel Nosheny, Miriam Ashford, Derek Flenniken, Adrienne Kormos, Robert C. Green, Tom Montine, Cat Conti, Ronald Petersen, Paul Aisen, Michael Rafii, Rema Raman, Gustavo Jimenez, Michael Donohue, Devon Gessert, Jennifer Salazar, Caileigh Zimmerman, Yuliana Cabrera, Sarah Walter, Garrett Miller, Godfrey Coker, Taylor Clanton, Lindsey Hergesheimer, Stephanie Smith, Olusegun Adegoke, Payam Mahboubi, Shelley Moore, Jeremy Pizzola, Elizabeth Shaffer, Brittany Sloan, Laurel Beckett, Danielle Harvey, Michael Donohue, Clifford R. Jack, Arvin Forghanian‐Arani, Bret Borowski, Chad Ward, Christopher Schwarz, David Jones, Jeff Gunter, Kejal Kantarci, Matthew Senjem, Prashanthi Vemuri, Robert Reid, Nick C. Fox, Ian Malone, Paul Thompson, Sophia I. Thomopoulos, Talia M. Nir, Neda Jahanshad, Charles DeCarli, Alexander Knaack, Evan Fletcher, Danielle Harvey, Duygu Tosun‐Turgut, Stephanie Rossi Chen, Mark Choe, Karen Crawford, Paul A. Yushkevich","doi":"10.1111/sjos.12660","DOIUrl":"https://doi.org/10.1111/sjos.12660","url":null,"abstract":"Abstract We propose a new approach, called as functional deep neural network (FDNN), for classifying multidimensional functional data. Specifically, a deep neural network is trained based on the principal components of the training data which shall be used to predict the class label of a future data function. Unlike the popular functional discriminant analysis approaches which only work for one‐dimensional functional data, the proposed FDNN approach applies to general non‐Gaussian multidimensional functional data. Moreover, when the log density ratio possesses a locally connected functional modular structure, we show that FDNN achieves minimax optimality. The superiority of our approach is demonstrated through both simulated and real‐world datasets.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136350260","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}
Shrijita Bhattacharya, Francois Kamper, J. Beirlant
Whether an extreme observation is an outlier or not depends strongly on the corresponding tail behavior of the underlying distribution. We develop an automatic, data‐driven method rooted in the mathematical theory of extremes to identify observations that deviate from the intermediate and central characteristics. The proposed algorithm is an extension of a method previously proposed in the literature for the specific case of heavy tailed Pareto‐type distributions to all max‐domains of attraction. We propose some applications such as a tail‐adjusted boxplot which yields a more accurate representation of possible outliers, and the identification of outliers in a multivariate context through an analysis of associated random variables such as local outlier factors. Several examples and simulation results illustrate the finite sample behavior of the algorithm and its applications.
{"title":"Outlier detection based on extreme value theory and applications","authors":"Shrijita Bhattacharya, Francois Kamper, J. Beirlant","doi":"10.1111/sjos.12665","DOIUrl":"https://doi.org/10.1111/sjos.12665","url":null,"abstract":"Whether an extreme observation is an outlier or not depends strongly on the corresponding tail behavior of the underlying distribution. We develop an automatic, data‐driven method rooted in the mathematical theory of extremes to identify observations that deviate from the intermediate and central characteristics. The proposed algorithm is an extension of a method previously proposed in the literature for the specific case of heavy tailed Pareto‐type distributions to all max‐domains of attraction. We propose some applications such as a tail‐adjusted boxplot which yields a more accurate representation of possible outliers, and the identification of outliers in a multivariate context through an analysis of associated random variables such as local outlier factors. Several examples and simulation results illustrate the finite sample behavior of the algorithm and its applications.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"1466 - 1502"},"PeriodicalIF":1.0,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46062864","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}
. We consider a stochastic system of N interacting particles with constant di(cid:27)usion coe(cid:30)cient and drift linear in space, time-depending on two unknown deterministic functions. Our concern here is the nonparametric estimation of these functions from a continuous observation of the process on [0 , T ] for (cid:28)xed T and large N . We de(cid:28)ne two collections of projection estimators belonging to (cid:28)nite-dimensional subspaces of L 2 ([0 , T ]) . We study the L 2 -risks of these estimators, where the risk is de(cid:28)ned either by the expectation of an empirical norm or by the expectation of a deterministic norm. Afterwards, we propose a data-driven choice of the dimensions and study the risk of the adaptive estimators. The results are illustrated by numerical experiments on simulated data.
{"title":"Nonparametric adaptive estimation for Interacting particle systems","authors":"F. Comte, V. Genon-Catalot","doi":"10.1111/sjos.12661","DOIUrl":"https://doi.org/10.1111/sjos.12661","url":null,"abstract":". We consider a stochastic system of N interacting particles with constant di(cid:27)usion coe(cid:30)cient and drift linear in space, time-depending on two unknown deterministic functions. Our concern here is the nonparametric estimation of these functions from a continuous observation of the process on [0 , T ] for (cid:28)xed T and large N . We de(cid:28)ne two collections of projection estimators belonging to (cid:28)nite-dimensional subspaces of L 2 ([0 , T ]) . We study the L 2 -risks of these estimators, where the risk is de(cid:28)ned either by the expectation of an empirical norm or by the expectation of a deterministic norm. Afterwards, we propose a data-driven choice of the dimensions and study the risk of the adaptive estimators. The results are illustrated by numerical experiments on simulated data.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48367198","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, with an assumed parametric model for the selection probability function, a robust model averaging estimation method is proposed for partially linear models with responses missing at random. The method is based on a weighted Mallows‐type criterion. The method is robust in the sense that the asymptotic optimality holds true as long as the true model of the selection probability function is some measurable function of its assumed model. The optimal weight vector for model averaging is obtained by minimizing the weighted Mallows‐type criterion. It is shown that the robust model averaging method achieves the lowest possible squared error asymptotically. Some simulation studies were conducted to evaluate the proposed method. An application to two real examples are provided as illustration.
{"title":"A robust model averaging approach for partially linear models with responses missing at random","authors":"Zhongqi Liang, Qihua Wang","doi":"10.1111/sjos.12659","DOIUrl":"https://doi.org/10.1111/sjos.12659","url":null,"abstract":"In this paper, with an assumed parametric model for the selection probability function, a robust model averaging estimation method is proposed for partially linear models with responses missing at random. The method is based on a weighted Mallows‐type criterion. The method is robust in the sense that the asymptotic optimality holds true as long as the true model of the selection probability function is some measurable function of its assumed model. The optimal weight vector for model averaging is obtained by minimizing the weighted Mallows‐type criterion. It is shown that the robust model averaging method achieves the lowest possible squared error asymptotically. Some simulation studies were conducted to evaluate the proposed method. An application to two real examples are provided as illustration.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49286763","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}
This aligns with efficiency bound targeted in the proof within the online supplement. Second, in equation (26), there is an errant qi included into the right-hand side of the second constraint that should be removed. Finally, the description of the hdCBPS in Section 5.2 requires clarification. The itemized entry should instead state “An augmented version of CBPS that extends (34) by using regularized regression techniques to find debiased estimates of the potential outcome means.” The new wording better reflects the hdCBPS method versus the original description.
{"title":"Errata for “A framework for covariate balance using Bregman distances”","authors":"","doi":"10.1111/sjos.12657","DOIUrl":"https://doi.org/10.1111/sjos.12657","url":null,"abstract":"This aligns with efficiency bound targeted in the proof within the online supplement. Second, in equation (26), there is an errant qi included into the right-hand side of the second constraint that should be removed. Finally, the description of the hdCBPS in Section 5.2 requires clarification. The itemized entry should instead state “An augmented version of CBPS that extends (34) by using regularized regression techniques to find debiased estimates of the potential outcome means.” The new wording better reflects the hdCBPS method versus the original description.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49009937","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 some clinical studies patient survival beyond a specific point in time, t0$$ {t}_0 $$ , say, may be of special interest as it may for instance indicate patient cure. To analyze the t0$$ {t}_0 $$ ‐year risk for such patients may be accomplished using logistic regression with appropriate weights (IPWCC) that may further be augmented (AIPWCC) to improve efficiency. In this paper, we derive the most efficient estimator for this problem, which is different from the AIPWCC based on the full data efficient influence function. We first give the result for a survival endpoint and then generalize to the competing risk setting. The proposed estimators superior behavior is illustrated using simulations as well as applying it to some real data concerning the survival of blood and marrow transplanted patients.
{"title":"Efficient\u0000 t\u0000 0\u0000 ‐year risk regression using the logistic model","authors":"T. Martinussen, T. Scheike","doi":"10.1111/sjos.12658","DOIUrl":"https://doi.org/10.1111/sjos.12658","url":null,"abstract":"In some clinical studies patient survival beyond a specific point in time, t0$$ {t}_0 $$ , say, may be of special interest as it may for instance indicate patient cure. To analyze the t0$$ {t}_0 $$ ‐year risk for such patients may be accomplished using logistic regression with appropriate weights (IPWCC) that may further be augmented (AIPWCC) to improve efficiency. In this paper, we derive the most efficient estimator for this problem, which is different from the AIPWCC based on the full data efficient influence function. We first give the result for a survival endpoint and then generalize to the competing risk setting. The proposed estimators superior behavior is illustrated using simulations as well as applying it to some real data concerning the survival of blood and marrow transplanted patients.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45028261","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：