{"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":"Network vector autoregressive moving average model","authors":"Xiao Chen, Yu Chen, Xixu Hu","doi":"10.4310/22-sii747","DOIUrl":"https://doi.org/10.4310/22-sii747","url":null,"abstract":"","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71152682","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":null,"pages":null},"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}
{"title":"Robust conditional spectral analysis of replicated time series","authors":"Zeda Li","doi":"10.4310/21-sii698","DOIUrl":"https://doi.org/10.4310/21-sii698","url":null,"abstract":"Classical second-order spectral analysis, which is based on the Fourier transform of the autocovariance functions, focuses on summarizing the oscillatory behaviors of a time series. However, this type of analysis is subject to two major limitations: first, being covariance-based, it cannot captures oscillatory information beyond the second moment, such as time-irreversibility and kurtosis, and cannot accommodate heavy-tail dependence and infinite variance; second, focusing on a single time series, it is unable to quantify the association between multiple time series and other covariates of interests. In this article, we propose a novel nonparametric approach to the spectral analysis of multiple time series and the associated covariates. The procedure is based on the copula spectral density kernel, which inherits the robust-ness properties of quantile regression and does not require any distributional assumptions such as the existence of finite moments. Copula spectral density kernels of different pairs are modeled jointly as a matrix to allow flexible smoothing. Through a tensor-product spline model of Cholesky components of the conditional copula spectral density matrix, the approach provides flexible nonparametric estimates of the copula spectral density matrix as nonparametric functions of frequency and covariate while preserving geometric con-straints. Empirical performance is evaluated in simulation studies and illustrated through an analysis of stride interval time series.","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71151106","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":"An iterative algorithm with adaptive weights and sparse Laplacian shrinkage for regression problems","authors":"Xingyu Chen, Yuehan Yang","doi":"10.4310/22-sii732","DOIUrl":"https://doi.org/10.4310/22-sii732","url":null,"abstract":"","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71152067","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":"Two-stage multivariate dynamic linear models to extract environmental and climate signals in coastal ecosystem data","authors":"J. Strock, G. Puggioni, S. Menden‐Deuer","doi":"10.4310/22-sii731","DOIUrl":"https://doi.org/10.4310/22-sii731","url":null,"abstract":"","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71152401","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}