{"title":"Measures of Uncertainty for Shrinkage Model Selection","authors":"Yuanyuan Li, Jiming Jiang","doi":"10.5705/ss.202021.0281","DOIUrl":"https://doi.org/10.5705/ss.202021.0281","url":null,"abstract":"","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70937682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: We propose a functional threshold autoregressive model for flexible functional time series modeling. In particular, the behavior of a function at a given time point can be described by different autoregressive mechanisms, depending on the values of a threshold variable at a past time point. Sufficient conditions for the strict stationarity and ergodicity of the functional threshold autoregressive process are investigated. We develop a novel criterion-based method simultaneously conducting dimension reduction and estimating the thresholds, autoregressive orders, and model parameters. We also establish the consistency and asymptotic distributions of the estimators of both thresholds and the underlying autoregressive models. Simulation studies and an application to U.S. Treasury zero-coupon yield rates are provided to illustrate the effectiveness and usefulness of the proposed methodology.
{"title":"Functional Threshold Autoregressive Model","authors":"Yuanbo Li, Kun Chen, Xunze Zheng, C. Yau","doi":"10.5705/ss.202022.0096","DOIUrl":"https://doi.org/10.5705/ss.202022.0096","url":null,"abstract":": We propose a functional threshold autoregressive model for flexible functional time series modeling. In particular, the behavior of a function at a given time point can be described by different autoregressive mechanisms, depending on the values of a threshold variable at a past time point. Sufficient conditions for the strict stationarity and ergodicity of the functional threshold autoregressive process are investigated. We develop a novel criterion-based method simultaneously conducting dimension reduction and estimating the thresholds, autoregressive orders, and model parameters. We also establish the consistency and asymptotic distributions of the estimators of both thresholds and the underlying autoregressive models. Simulation studies and an application to U.S. Treasury zero-coupon yield rates are provided to illustrate the effectiveness and usefulness of the proposed methodology.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70938567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: The rank-tracking probability (RTP) is a useful statistical index for measuring the “tracking ability” of longitudinal disease risk factors in biomedical studies. A flexible nonparametric method for estimating the RTP is the two-step un-structured kernel smoothing estimator, which can be applied when there are time-invariant and categorical covariates. We propose a dynamic copula-based smoothing method for estimating the RTP, and show that it is both theoretically and practically superior to the unstructured smoothing method. We derive the asymptotic mean squared errors of the copula-based kernel smoothing estimators, and use a simulation study to show that the proposed method has smaller empirical mean squared errors than those of the unstructured smoothing method. We apply the proposed estimation method to a longitudinal epidemiological study and show that it leads to clinically meaningful findings in biomedical applications.
摘要:在生物医学研究中，Rank-Tracking probability (RTP)是衡量纵向疾病危险因素“跟踪能力”的一个有用的统计指标。估计RTP的一种灵活的非参数方法是两步非结构化核平滑估计器(Wu and Tian, 2013)，它可以应用于存在时不变协变量和分类协变量的情况。本文提出了一种基于动态公式的平滑方法来估计RTP，并证明了该方法在理论和实践上都优于非结构化平滑方法。我们推导了基于copula的核平滑估计的渐近均方误差，并通过仿真研究证明了基于copula的平滑方法比非结构化平滑方法具有更小的经验均方误差。我们将提出的估计方法应用于纵向流行病学研究，并表明它在生物医学应用中导致临床有意义的发现。
{"title":"Dynamic Copula-Based Nonparametric Estimation of Rank-Tracking Probabilities With Longitudinal Data","authors":"Xiaoyu Zhang, Mixia Wu, Colin O. Wu","doi":"10.5705/ss.202021.0422","DOIUrl":"https://doi.org/10.5705/ss.202021.0422","url":null,"abstract":": The rank-tracking probability (RTP) is a useful statistical index for measuring the “tracking ability” of longitudinal disease risk factors in biomedical studies. A flexible nonparametric method for estimating the RTP is the two-step un-structured kernel smoothing estimator, which can be applied when there are time-invariant and categorical covariates. We propose a dynamic copula-based smoothing method for estimating the RTP, and show that it is both theoretically and practically superior to the unstructured smoothing method. We derive the asymptotic mean squared errors of the copula-based kernel smoothing estimators, and use a simulation study to show that the proposed method has smaller empirical mean squared errors than those of the unstructured smoothing method. We apply the proposed estimation method to a longitudinal epidemiological study and show that it leads to clinically meaningful findings in biomedical applications.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70938132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Test for Zero Mean of Errors In An ARMA-GGARCH Model After Using A Median Inference Abstract: The stylized fact of heavy tails makes median inferences appealing in fitting an ARMA model with heteroscedastic errors to financial returns. To ensure that the model still concerns the conditional mean, we test for a zero mean of the errors using a random weighted bootstrap method for quantifying estimation uncertainty. The proposed test is robust against heteroscedasticity and heavy tails as we do not infer the heteroscedasticity and need fewer finite moments. Simulations confirm the good finite sample performance in terms of size and power. Empirical applications caution the model interpretation after using a median inference.
{"title":"Test for Zero Mean of Errors In An ARMA-GGARCH Model After Using A Median Inference","authors":"Yaolan Ma, Mo Zhou, Liang Peng, Rongmao Zhang","doi":"10.5705/ss.202022.0013","DOIUrl":"https://doi.org/10.5705/ss.202022.0013","url":null,"abstract":"Test for Zero Mean of Errors In An ARMA-GGARCH Model After Using A Median Inference Abstract: The stylized fact of heavy tails makes median inferences appealing in fitting an ARMA model with heteroscedastic errors to financial returns. To ensure that the model still concerns the conditional mean, we test for a zero mean of the errors using a random weighted bootstrap method for quantifying estimation uncertainty. The proposed test is robust against heteroscedasticity and heavy tails as we do not infer the heteroscedasticity and need fewer finite moments. Simulations confirm the good finite sample performance in terms of size and power. Empirical applications caution the model interpretation after using a median inference.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70937873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Robust Estimation of Covariance Matrices: Adversarial Contamination and Beyond","authors":"Stanislav Minsker, Lang Wang","doi":"10.5705/ss.202021.0388","DOIUrl":"https://doi.org/10.5705/ss.202021.0388","url":null,"abstract":"","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70937901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ying Sheng, Yifei Sun, C. E. Mcculloch, Chiung-Yu Huang
Scalable Estimation for High Velocity Survival Data Able to Accommodate Addition of Covariates Abstract: With the rapidly increasing availability of large-scale streaming data, there has been a growing interest in developing methods that allow the processing of the data in batches without requiring storage of the full dataset. In this paper, we propose a hybrid likelihood approach for scalable estimation of the Cox model using individual-level data in the current data batch and summary statistics calculated from historical data. We show that the proposed scalable estimator is asymptotically as efficient as the maximum likelihood estimator calculated using the entire dataset with low data storage requirements and low loading and computation time. A challenge in analyzing survival data batches that is not accommodated in ex-tant methods is that new covariates may become available midway through data collection. To accommodate addition of covariates, we develop a hybrid empirical likelihood approach to incorporate the historical covariate effects evaluated in a reduced Cox model. The extended scalable estimator is asymptotically more efficient than the maximum likelihood estimator obtained using only the data batches that include the additional covariates. The proposed approaches are evaluated by numerical simulations and illustrated with an analysis of Surveillance, Epidemiology, and End Results breast data.
{"title":"Scalable Estimation for High Velocity Survival Data Able to Accommodate Addition of Covariates","authors":"Ying Sheng, Yifei Sun, C. E. Mcculloch, Chiung-Yu Huang","doi":"10.5705/ss.202022.0028","DOIUrl":"https://doi.org/10.5705/ss.202022.0028","url":null,"abstract":"Scalable Estimation for High Velocity Survival Data Able to Accommodate Addition of Covariates Abstract: With the rapidly increasing availability of large-scale streaming data, there has been a growing interest in developing methods that allow the processing of the data in batches without requiring storage of the full dataset. In this paper, we propose a hybrid likelihood approach for scalable estimation of the Cox model using individual-level data in the current data batch and summary statistics calculated from historical data. We show that the proposed scalable estimator is asymptotically as efficient as the maximum likelihood estimator calculated using the entire dataset with low data storage requirements and low loading and computation time. A challenge in analyzing survival data batches that is not accommodated in ex-tant methods is that new covariates may become available midway through data collection. To accommodate addition of covariates, we develop a hybrid empirical likelihood approach to incorporate the historical covariate effects evaluated in a reduced Cox model. The extended scalable estimator is asymptotically more efficient than the maximum likelihood estimator obtained using only the data batches that include the additional covariates. The proposed approaches are evaluated by numerical simulations and illustrated with an analysis of Surveillance, Epidemiology, and End Results breast data.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70938004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jianling Wang, Thuan Nguyen, Y. Luan, Jiming Jiang
: The mean squared prediction error (MSPE) is an important measure of uncertainty in small-area estimation. It is desirable to produce a second-order unbiased MSPE estimator, that is, the bias of the estimator is o ( m − 1 ), where m is the total number of small areas for which data are available. However, this is difficult, especially if the estimator needs to be positive, or at least nonnegative. In fact, very few MSPE estimators are both second-order unbiased and guaranteed to be positive. We consider an alternative, easier approach of estimating the logarithm of the MSPE (log-MSPE), thus avoiding the positivity problem. We derive a second-order unbiased estimator of the log-MSPE using the Prasad–Rao linearization method. The results of empirical studies demonstrate the superiority of the proposed log-MSPE estimator over a naive log-MSPE estimator and an existing method, known as McJack. Lastly, we demonstrate the proposed method by applying it to real data.
{"title":"On Estimation of the Logarithm of the Mean Squared Prediction Error of A Mixed-effect Predictor","authors":"Jianling Wang, Thuan Nguyen, Y. Luan, Jiming Jiang","doi":"10.5705/ss.202022.0043","DOIUrl":"https://doi.org/10.5705/ss.202022.0043","url":null,"abstract":": The mean squared prediction error (MSPE) is an important measure of uncertainty in small-area estimation. It is desirable to produce a second-order unbiased MSPE estimator, that is, the bias of the estimator is o ( m − 1 ), where m is the total number of small areas for which data are available. However, this is difficult, especially if the estimator needs to be positive, or at least nonnegative. In fact, very few MSPE estimators are both second-order unbiased and guaranteed to be positive. We consider an alternative, easier approach of estimating the logarithm of the MSPE (log-MSPE), thus avoiding the positivity problem. We derive a second-order unbiased estimator of the log-MSPE using the Prasad–Rao linearization method. The results of empirical studies demonstrate the superiority of the proposed log-MSPE estimator over a naive log-MSPE estimator and an existing method, known as McJack. Lastly, we demonstrate the proposed method by applying it to real data.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70938735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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：