Regression models with functional responses and covariates have attracted extensive research. Nevertheless, there is no existing method for the situation where the functional covariates are bivariate functions with one of the variables in common with the response function. In this article, we propose a nonparametric function-on-function regression method. We construct model spaces using a Gaussian kernel function and smoothing spline ANOVA decomposition. We estimate the nonparametric function using penalized likelihood and study properties of the Gaussian kernel function and the convergence rate of the proposed estimation method. We evaluate the proposed methods using simulations and illustrate them using two real data examples.
{"title":"A nonparametric concurrent regression model with multivariate functional inputs","authors":"Yutong Zhai, Zhanfeng Wang, Yuedong Wang","doi":"10.4310/23-sii782","DOIUrl":"https://doi.org/10.4310/23-sii782","url":null,"abstract":"Regression models with functional responses and covariates have attracted extensive research. Nevertheless, there is no existing method for the situation where the functional covariates are bivariate functions with one of the variables in common with the response function. In this article, we propose a nonparametric function-on-function regression method. We construct model spaces using a Gaussian kernel function and smoothing spline ANOVA decomposition. We estimate the nonparametric function using penalized likelihood and study properties of the Gaussian kernel function and the convergence rate of the proposed estimation method. We evaluate the proposed methods using simulations and illustrate them using two real data examples.","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":"12 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525586","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}
Many association analysis methods have been developed to detect disease related rare genetic variants or gene-environment interactions. Most of them are based on prospectively likelihood, so they are robust but might not be powerful enough. On the other hand, retrospective likelihood based methods assuming gene-environment independence can effectively improve the association test power, but they suffer from type‑I error rate inflation if the independence assumption is violated. The aim of this paper is to develop novel test methods to balance power and robustness by appropriately weighting the above retrospective likelihood based tests and the existing prospective likelihood based tests. The desired finite sample performances of the proposed methods are demonstrated through simulation studies and the application to a real dataset.
{"title":"Robust and powerful gene-environment interaction tests using rare genetic variants in case-control studies","authors":"Yanan Zhao, Hong Zhang","doi":"10.4310/23-sii800","DOIUrl":"https://doi.org/10.4310/23-sii800","url":null,"abstract":"Many association analysis methods have been developed to detect disease related rare genetic variants or gene-environment interactions. Most of them are based on prospectively likelihood, so they are robust but might not be powerful enough. On the other hand, retrospective likelihood based methods assuming gene-environment independence can effectively improve the association test power, but they suffer from type‑I error rate inflation if the independence assumption is violated. The aim of this paper is to develop novel test methods to balance power and robustness by appropriately weighting the above retrospective likelihood based tests and the existing prospective likelihood based tests. The desired finite sample performances of the proposed methods are demonstrated through simulation studies and the application to a real dataset.","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":"39 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525567","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 paper considers the problem of parameter estimation in the accelerated failure time model with divergent number of parameters under fixed design. We propose an estimator based on the general relative error criterion. We show that the proposed estimator is consistent and asymptotically normal under mild regular conditions. We also propose a variable selection procedure and show its oracle property as well as the consistency of model selection. Numerical studies have been conducted to compare the performance of different general relative error based estimators.
{"title":"Asymptotic properties of relative error estimation for accelerated failure time model with divergent number of parameters","authors":"Fei Ye, Hongyi Zhou, Ying Yang","doi":"10.4310/23-sii816","DOIUrl":"https://doi.org/10.4310/23-sii816","url":null,"abstract":"The paper considers the problem of parameter estimation in the accelerated failure time model with divergent number of parameters under fixed design. We propose an estimator based on the general relative error criterion. We show that the proposed estimator is consistent and asymptotically normal under mild regular conditions. We also propose a variable selection procedure and show its oracle property as well as the consistency of model selection. Numerical studies have been conducted to compare the performance of different general relative error based estimators.","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525573","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 study the generalized linear mixed models with an unknown link function for correlated outcome data. We propose sieve maximum likelihood estimation procedures by using B‑splines. Specifically, we estimate the unknown link function in a sieve space spanned by the B‑spline basis of the linear predictor that includes both the fixed and random terms. We establish the consistency and asymptotic normality of the proposed sieve maximum likelihood estimators. Extensive simulation studies, along with an application to an epileptic study, are provided to evaluate the finite-sample performance of the proposed method.
{"title":"Sieve maximum likelihood estimation for generalized linear mixed models with an unknown link function","authors":"Guoqing Diao, Mengdie Yuan","doi":"10.4310/23-sii813","DOIUrl":"https://doi.org/10.4310/23-sii813","url":null,"abstract":"We study the generalized linear mixed models with an unknown link function for correlated outcome data. We propose sieve maximum likelihood estimation procedures by using B‑splines. Specifically, we estimate the unknown link function in a sieve space spanned by the B‑spline basis of the linear predictor that includes both the fixed and random terms. We establish the consistency and asymptotic normality of the proposed sieve maximum likelihood estimators. Extensive simulation studies, along with an application to an epileptic study, are provided to evaluate the finite-sample performance of the proposed method.","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":"68 7-8","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525576","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 paper addresses the problem of abnormal sample detection in deep learning-based computer vision, focusing on two types of abnormal samples: outlier samples and adversarial samples. The presence of these abnormal samples can significantly degrade the performance and robustness of deep learning models, posing security risks in critical areas. To address this, we propose a method that combines robust Mahalanobis distance (RMD) estimation with a pretrained convolutional neural networks (CNNs) model. The RMD estimation involves using minimum covariance matrix determinant (MCD), $T$-type, and $S$ estimators. Furthermore, we theoretically analyze the breakdown point and influence function of the $T$-type estimator. To evaluate the effectiveness and robustness of our method, we utilize public datasets, CNN models, and adversarial sample generation algorithms commonly employed in the field. The experimental results demonstrate the effectiveness of our algorithm in detecting abnormal samples.
{"title":"Abnormal sample detection based on robust Mahalanobis distance estimation in adversarial machine learning","authors":"Wan Tian, Lingyue Zhang, Hengjian Cui","doi":"10.4310/23-sii818","DOIUrl":"https://doi.org/10.4310/23-sii818","url":null,"abstract":"This paper addresses the problem of abnormal sample detection in deep learning-based computer vision, focusing on two types of abnormal samples: outlier samples and adversarial samples. The presence of these abnormal samples can significantly degrade the performance and robustness of deep learning models, posing security risks in critical areas. To address this, we propose a method that combines robust Mahalanobis distance (RMD) estimation with a pretrained convolutional neural networks (CNNs) model. The RMD estimation involves using minimum covariance matrix determinant (MCD), $T$-type, and $S$ estimators. Furthermore, we theoretically analyze the breakdown point and influence function of the $T$-type estimator. To evaluate the effectiveness and robustness of our method, we utilize public datasets, CNN models, and adversarial sample generation algorithms commonly employed in the field. The experimental results demonstrate the effectiveness of our algorithm in detecting abnormal samples.","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":"66 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525580","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 offer a review and bibliography of work on Hankel low-rank approximation and completion, with particular emphasis on how this methodology can be used for time series analysis and forecasting.We begin by describing possible formulations of the problem and offer commentary on related topics and challenges in obtaining globally optimal solutions. Key theorems are provided, and the paper closes with some expository examples.
{"title":"Hankel low-rank approximation and completion in time series analysis and forecasting: a brief review","authors":"Jonathan Gillard, Konstantin Usevich","doi":"10.4310/22-sii735","DOIUrl":"https://doi.org/10.4310/22-sii735","url":null,"abstract":"In this paper we offer a review and bibliography of work on Hankel low-rank approximation and completion, with particular emphasis on how this methodology can be used for time series analysis and forecasting.We begin by describing possible formulations of the problem and offer commentary on related topics and challenges in obtaining globally optimal solutions. Key theorems are provided, and the paper closes with some expository examples.","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":"53 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525554","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}
Mark B. Fiecas, Christian Coffman, Meng Xu, Timothy J. Hendrickson, Bryon A. Mueller, Bonnie Klimes-Dougan, Kathryn R. Cullen
Motivated by a study on adolescent mental health, we conduct a dynamic connectivity analysis using resting-state functional magnetic resonance imaging (fMRI) data. A dynamic connectivity analysis investigates how the interactions between different regions of the brain, represented by the different dimensions of a multivariate time series, change over time. HiddenMarkov models (HMMs) and hidden semi-Markov models (HSMMs) are common analytic approaches for conducting dynamic connectivity analyses. However, existing approaches for HSMMs are limited in their ability to incorporate covariate information. In this work, we approximate an HSMM using an HMM for modeling multivariate time series data. The approximate HSMM (aHSMM) model allows one to explicitly model dwell-time distributions that are available to HSMMs, while maintaining the theoretical and methodological advances that are available to HMMs. We conducted a simulation study to show the performance of the aHSMM relative to other approaches. Finally, we used the aHSMM to conduct a dynamic connectivity analysis, where we showed how dwell-time distributions vary across the severity of non-suicidal self-injury (NSSI) in adolescents. The aHSMM allowed us to identify states that have greater dwell-times for those with moderate or severe NSSI.
{"title":"Approximate hidden semi-Markov models for dynamic connectivity analysis in resting-state fMRI","authors":"Mark B. Fiecas, Christian Coffman, Meng Xu, Timothy J. Hendrickson, Bryon A. Mueller, Bonnie Klimes-Dougan, Kathryn R. Cullen","doi":"10.4310/22-sii730","DOIUrl":"https://doi.org/10.4310/22-sii730","url":null,"abstract":"Motivated by a study on adolescent mental health, we conduct a dynamic connectivity analysis using resting-state functional magnetic resonance imaging (fMRI) data. A dynamic connectivity analysis investigates how the interactions between different regions of the brain, represented by the different dimensions of a multivariate time series, change over time. HiddenMarkov models (HMMs) and hidden semi-Markov models (HSMMs) are common analytic approaches for conducting dynamic connectivity analyses. However, existing approaches for HSMMs are limited in their ability to incorporate covariate information. In this work, we approximate an HSMM using an HMM for modeling multivariate time series data. The approximate HSMM (aHSMM) model allows one to explicitly model dwell-time distributions that are available to HSMMs, while maintaining the theoretical and methodological advances that are available to HMMs. We conducted a simulation study to show the performance of the aHSMM relative to other approaches. Finally, we used the aHSMM to conduct a dynamic connectivity analysis, where we showed how dwell-time distributions vary across the severity of non-suicidal self-injury (NSSI) in adolescents. The aHSMM allowed us to identify states that have greater dwell-times for those with moderate or severe NSSI.","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":"105 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525553","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}
Existing time series analysis and forecasting approaches struggle to produce accurate results in application to time series with complex trend, such as those commonly displayed by indices of industrial production (IIPs). In this study, a new version of the Singular Spectrum Analysis (SSA) technique is developed, namely the Separate Trend and Seasonality (SSA-STS) forecasting algorithm. Its performance is compared to those of benchmark, classical times series forecasting methods, including Basic SSA (the core version of SSA), ARIMA, Exponential Smoothing (ETS) and Neural Network (NN). The methods in this study are applied to both simulated and real data. The latter includes twenty four monthly series of seasonally unadjusted IIPs of various sectors for the UK, Germany and France. Using the out-of-sample forecasts, the results of this newly developed SSA-STS algorithm were compared to the other aforemen-tioned forecasting schemes by the means of pooled Root-Mean-Square-Error (RMSE). The pooling is done based on the number of steps ahead the forecasts extend, allowing for the performance of the methods to be evaluated on short and long horizons. The Kolmogorov-Smirnov Predictive Accuracy (KSPA) statistical test is applied to certify whether the errors produced by SSA-STS are statistically significantly smaller than those of all the benchmark methods. Since this new technique is based on separate trend and seasonality forecasting, it overcomes the difficulties in forecasting series with complex trends and seasonality, thus demonstrating a clear advantage over other methods in such particular cases.
{"title":"Forecasting industrial production indices with a new singular spectrum analysis forecasting algorithm","authors":"Sofia Borodich Suarez, S. Heravi, A. Pepelyshev","doi":"10.4310/21-sii693","DOIUrl":"https://doi.org/10.4310/21-sii693","url":null,"abstract":"Existing time series analysis and forecasting approaches struggle to produce accurate results in application to time series with complex trend, such as those commonly displayed by indices of industrial production (IIPs). In this study, a new version of the Singular Spectrum Analysis (SSA) technique is developed, namely the Separate Trend and Seasonality (SSA-STS) forecasting algorithm. Its performance is compared to those of benchmark, classical times series forecasting methods, including Basic SSA (the core version of SSA), ARIMA, Exponential Smoothing (ETS) and Neural Network (NN). The methods in this study are applied to both simulated and real data. The latter includes twenty four monthly series of seasonally unadjusted IIPs of various sectors for the UK, Germany and France. Using the out-of-sample forecasts, the results of this newly developed SSA-STS algorithm were compared to the other aforemen-tioned forecasting schemes by the means of pooled Root-Mean-Square-Error (RMSE). The pooling is done based on the number of steps ahead the forecasts extend, allowing for the performance of the methods to be evaluated on short and long horizons. The Kolmogorov-Smirnov Predictive Accuracy (KSPA) statistical test is applied to certify whether the errors produced by SSA-STS are statistically significantly smaller than those of all the benchmark methods. Since this new technique is based on separate trend and seasonality forecasting, it overcomes the difficulties in forecasting series with complex trends and seasonality, thus demonstrating a clear advantage over other methods in such particular cases.","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71150887","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":"SIMEX estimation for quantile regression model with measurement error","authors":"Yiping Yang, Peixin Zhao, Dongsheng Wu","doi":"10.4310/22-sii742","DOIUrl":"https://doi.org/10.4310/22-sii742","url":null,"abstract":"","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71152909","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：