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":"1 1","pages":""},"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}
{"title":"On Combining Individual-Level Data With Summary Data in Statistical Inferences","authors":"Lu Deng, Sheng Fu, J. Qin, Kai Yu","doi":"10.5705/ss.202022.0228","DOIUrl":"https://doi.org/10.5705/ss.202022.0228","url":null,"abstract":"On Combining Individual-Level Data With Summary Data in Statistical Inferences","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"34 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70939106","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}
: Motivated by studying the asymptotic properties of the parameter estimator in switching linear state space models, switching GARCH models, switching stochastic volatility models, and recurrent neural networks, we investigate the maximum likelihood estimator for general Markov switching models. To this end, we first propose an innovative matrix-valued Markovian iterated function system (MIFS) representation for the likelihood function. Then, we express the derivatives of the MIFS as a composition of random matrices. To the best of our knowledge, this is a new method in the literature. Using this useful device, we establish the strong consistency and asymptotic normality of the maximum likelihood estimator under some regularity conditions. Furthermore, we characterize the Fisher information as the inverse of the asymptotic variance.
{"title":"Asymptotic Behavior of the Maximum Likelihood Estimator for General Markov Switching Models","authors":"C. Fuh, T. Pang","doi":"10.5705/ss.202021.0336","DOIUrl":"https://doi.org/10.5705/ss.202021.0336","url":null,"abstract":": Motivated by studying the asymptotic properties of the parameter estimator in switching linear state space models, switching GARCH models, switching stochastic volatility models, and recurrent neural networks, we investigate the maximum likelihood estimator for general Markov switching models. To this end, we first propose an innovative matrix-valued Markovian iterated function system (MIFS) representation for the likelihood function. Then, we express the derivatives of the MIFS as a composition of random matrices. To the best of our knowledge, this is a new method in the literature. Using this useful device, we establish the strong consistency and asymptotic normality of the maximum likelihood estimator under some regularity conditions. Furthermore, we characterize the Fisher information as the inverse of the asymptotic variance.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"23 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70937369","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}
This supplementary materials provides detailed proofs of Theorem 1 and 2 and Proposition 1-3 as well as the power simulation results under the heteroscedastic condition.
{"title":"An Adaptive Weighted Component Test for High-Dimensional Means","authors":"Yidi Qu, L. Shu, Jinfeng Xu","doi":"10.5705/ss.202022.0143","DOIUrl":"https://doi.org/10.5705/ss.202022.0143","url":null,"abstract":"This supplementary materials provides detailed proofs of Theorem 1 and 2 and Proposition 1-3 as well as the power simulation results under the heteroscedastic condition.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70938686","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":"Threshold Estimation in Proportional Mean Residual Life Model","authors":"Bing Wang, Xinyuan Song","doi":"10.5705/ss.202022.0017","DOIUrl":"https://doi.org/10.5705/ss.202022.0017","url":null,"abstract":"of the main","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70937929","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":"Homogeneity Tests for High-dimensional Mean Vectors and Covariance Matrices","authors":"Wenwen Guo, Xinyuan Song, H. Cui","doi":"10.5705/ss.202022.0048","DOIUrl":"https://doi.org/10.5705/ss.202022.0048","url":null,"abstract":"Homogeneity Tests","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70938322","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}
Wen Su, Li Liu, Guosheng Yin, Xingqiu Zhao, Ying Zhang
We study semiparametric regression for a recurrent event process with an informative terminal event, where observations are taken only at discrete time points, rather than continuously over time. To account for the effect of a terminal event on the recurrent event process, we propose a semiparametric reversed mean model, for which we develop a two-stage sieve likelihood-based method to estimate the baseline mean function and the covariate effects. Our approach overcomes the computational difficulties arising from the nuisance functional parameter in the assumption that the likelihood is based on a Poisson process. We establish the consistency, convergence rate, and asymptotic normality of the proposed two-stage estimator, which is robust against the assumption of an underlying Poisson process. The proposed method is evaluated using extensive simulation studies, and demonstrated using panel count data from a longitudinal healthy longevity study and data from a bladder tumor study.
{"title":"SEMIPARAMETRIC REVERSED MEAN MODEL FOR RECURRENT EVENT PROCESS WITH INFORMATIVE TERMINAL EVENT.","authors":"Wen Su, Li Liu, Guosheng Yin, Xingqiu Zhao, Ying Zhang","doi":"10.5705/ss.202021.0353","DOIUrl":"10.5705/ss.202021.0353","url":null,"abstract":"<p><p>We study semiparametric regression for a recurrent event process with an informative terminal event, where observations are taken only at discrete time points, rather than continuously over time. To account for the effect of a terminal event on the recurrent event process, we propose a semiparametric reversed mean model, for which we develop a two-stage sieve likelihood-based method to estimate the baseline mean function and the covariate effects. Our approach overcomes the computational difficulties arising from the nuisance functional parameter in the assumption that the likelihood is based on a Poisson process. We establish the consistency, convergence rate, and asymptotic normality of the proposed two-stage estimator, which is robust against the assumption of an underlying Poisson process. The proposed method is evaluated using extensive simulation studies, and demonstrated using panel count data from a longitudinal healthy longevity study and data from a bladder tumor study.</p>","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"1 1","pages":"1843-1862"},"PeriodicalIF":1.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12291165/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70937462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: In this paper, we propose an outlier detection procedure, based on a high-breakdown minimum ridge covariance determinant estimator that is especially useful for the large p/n scenario. The estimator is obtained from the subset of observations, after excluding potential outliers, by applying the so-called concentration steps. We explore the asymptotic distribution of the modified Mahalanobis distance related to the proposed estimator under certain moment conditions, and obtain a theoretical cutoff value for outlier identification. We also improve the outlier detection power by adding a one-step reweighting procedure. Lastly, we investigate the performance of the proposed methods using simulations and a real-data analysis.
{"title":"Outlier Detection via a Minimum Ridge Covariance Determinant Estimator","authors":"Chikun Li, B. Jin, Yuehua Wu","doi":"10.5705/ss.202022.0142","DOIUrl":"https://doi.org/10.5705/ss.202022.0142","url":null,"abstract":": In this paper, we propose an outlier detection procedure, based on a high-breakdown minimum ridge covariance determinant estimator that is especially useful for the large p/n scenario. The estimator is obtained from the subset of observations, after excluding potential outliers, by applying the so-called concentration steps. We explore the asymptotic distribution of the modified Mahalanobis distance related to the proposed estimator under certain moment conditions, and obtain a theoretical cutoff value for outlier identification. We also improve the outlier detection power by adding a one-step reweighting procedure. Lastly, we investigate the performance of the proposed methods using simulations and a real-data analysis.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70938675","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}
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