{"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}
{"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}
{"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}
{"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}
{"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
{"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}
{"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}
Anass El Yaagoubi Bourakna, Marco Pinto, Norbert Fortin, Hernando Ombao
{"title":"Smooth online parameter estimation for time varying VAR models with application to rat local field potential activity data.","authors":"Anass El Yaagoubi Bourakna, Marco Pinto, Norbert Fortin, Hernando Ombao","doi":"10.4310/22-sii729","DOIUrl":"10.4310/22-sii729","url":null,"abstract":"<p><p>Multivariate time series data appear often as realizations of non-stationary processes where the covariance matrix or spectral matrix smoothly evolve over time. Most of the current approaches estimate the time-varying spectral properties only retrospectively - that is, after the entire data has been observed. Retrospective estimation is a major limitation in many adaptive control applications where it is important to estimate these properties and detect changes in the system as they happen in real-time. To overcome this limitation, we develop an online estimation procedure that gives a real-time update of the time-varying parameters as new observations arrive. One approach to modeling non-stationary time series is to fit time-varying vector autoregressive models (tv-VAR). However, one major obstacle in online estimation of such models is the computational cost due to the high-dimensionality of the parameters. Existing methods such as the Kalman filter or local least squares are feasible. However, they are not always suitable because they provide noisy estimates and can become prohibitively costly as the dimension of the time series increases. In our brain signal application, it is critical to develop a robust method that can estimate, in real-time, the properties of the underlying stochastic process, in particular, the spectral brain connectivity measures. For these reasons we propose a new smooth online parameter estimation approach (SOPE) that has the ability to control for the smoothness of the estimates with a reasonable computational complexity. Consequently, the models are fit in real-time even for high dimensional time series. We demonstrate that our proposed SOPE approach is as good as the Kalman filter in terms of mean-squared error for small dimensions. However, unlike the Kalman filter, the SOPE has lower computational cost and hence scalable for higher dimensions. Finally, we apply the SOPE method to local field potential activity data from the hippocampus of a rat performing an odor sequence memory task. As demonstrated in the video, the proposed SOPE method is able to capture the dynamics of the connectivity as the rat samples the different odor stimuli.</p>","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":"1 1","pages":"227-257"},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12015553/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71152350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}