{"title":"Necessary and Sufficient Conditions for Multiple Objective Optimal Regression Designs","authors":"Lucy L. Gao, J. Ye, Shangzhi Zeng, Julie Zhou","doi":"10.5705/ss.202022.0328","DOIUrl":"https://doi.org/10.5705/ss.202022.0328","url":null,"abstract":"We typically construct optimal designs based on a single objective function. To better capture the breadth of an experiment's goals, we could instead construct a multiple objective optimal design based on multiple objective functions. While algorithms have been developed to find multi-objective optimal designs (e.g. efficiency-constrained and maximin optimal designs), it is far less clear how to verify the optimality of a solution obtained from an algorithm. In this paper, we provide theoretical results characterizing optimality for efficiency-constrained and maximin optimal designs on a discrete design space. We demonstrate how to use our results in conjunction with linear programming algorithms to verify optimality.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42471367","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}
Linh Nghiem, Francis K.C. Hui, Samuel Mueller, A.H.Welsh
{"title":"Sparse Sliced Inverse Regression via Cholesky Matrix Penalization","authors":"Linh Nghiem, Francis K.C. Hui, Samuel Mueller, A.H.Welsh","doi":"10.5705/ss.202020.0406","DOIUrl":"https://doi.org/10.5705/ss.202020.0406","url":null,"abstract":"We introduce a new sparse sliced inverse regression estimator called Cholesky matrix penalization and its adaptive version for achieving sparsity in estimating the dimensions of the central subspace. The new estimators use the Cholesky decomposition of the covariance matrix of the covariates and include a regularization term in the objective function to achieve sparsity in a computationally efficient manner. We establish the theoretical values of the tuning parameters that achieve estimation and variable selection consistency for the central subspace. Furthermore, we propose a new projection information criterion to select the tuning parameter for our proposed estimators and prove that the new criterion facilitates selection consistency. The Cholesky matrix penalization estimator inherits the strength of the Matrix Lasso and the Lasso sliced inverse regression estimator; it has superior performance in numerical studies and can be adapted to other sufficient dimension methods in the literature.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135181008","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":"That Prasad-Rao is Robust: Estimation of Mean Squared Prediction Error of Observed Best Predictor under Potential Model Misspecification","authors":"Xiaohui Liu, Haiqiang Ma, Jiming Jiang","doi":"10.5705/ss.202020.0325","DOIUrl":"https://doi.org/10.5705/ss.202020.0325","url":null,"abstract":"","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135181024","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 Construction of Nonregular Two-Level Factorial Designs With Maximum Generalized Resolutions","authors":"Chenlu Shi, Boxin Tang","doi":"10.5705/ss.202021.0024","DOIUrl":"https://doi.org/10.5705/ss.202021.0024","url":null,"abstract":"","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135182934","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":"Nonparametric Bayesian Two-Level Clustering for Subject-Level Single-Cell Expression Data","authors":"Qiuyu Wu, Xiangyu Luo","doi":"10.5705/ss.202020.0337","DOIUrl":"https://doi.org/10.5705/ss.202020.0337","url":null,"abstract":"The advent of single-cell sequencing opens new avenues for personalized treatment. In this paper, we address a two-level clustering problem of simultaneous subject subgroup discovery (subject level) and cell type detection (cell level) for single-cell expression data from multiple subjects. However, current statistical approaches either cluster cells without considering the subject heterogeneity or group subjects without using the single-cell information. To bridge the gap between cell clustering and subject grouping, we develop a nonparametric Bayesian model, Subject and Cell clustering for Single-Cell expression data (SCSC) model, to achieve subject and cell grouping simultaneously. SCSC does not need to prespecify the subject subgroup number or the cell type number. It automatically induces subject subgroup structures and matches cell types across subjects. Moreover, it directly models the single-cell raw count data by deliberately considering the data's dropouts, library sizes, and over-dispersion. A blocked Gibbs sampler is proposed for the posterior inference. Simulation studies and the application to a multi-subject iPSC scRNA-seq dataset validate the ability of SCSC to simultaneously cluster subjects and cells.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135181000","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}
Peiyao Wang, Quefeng Li, Dinggang Shen, Yufeng Liu
{"title":"HIGH-DIMENSIONAL FACTOR REGRESSION FOR HETEROGENEOUS SUBPOPULATIONS.","authors":"Peiyao Wang, Quefeng Li, Dinggang Shen, Yufeng Liu","doi":"10.5705/ss.202020.0145","DOIUrl":"10.5705/ss.202020.0145","url":null,"abstract":"<p><p>In modern scientific research, data heterogeneity is commonly observed owing to the abundance of complex data. We propose a factor regression model for data with heterogeneous subpopulations. The proposed model can be represented as a decomposition of heterogeneous and homogeneous terms. The heterogeneous term is driven by latent factors in different subpopulations. The homogeneous term captures common variation in the covariates and shares common regression coefficients across subpopulations. Our proposed model attains a good balance between a global model and a group-specific model. The global model ignores the data heterogeneity, while the group-specific model fits each subgroup separately. We prove the estimation and prediction consistency for our proposed estimators, and show that it has better convergence rates than those of the group-specific and global models. We show that the extra cost of estimating latent factors is asymptotically negligible and the minimax rate is still attainable. We further demonstrate the robustness of our proposed method by studying its prediction error under a mis-specified group-specific model. Finally, we conduct simulation studies and analyze a data set from the Alzheimer's Disease Neuroimaging Initiative and an aggregated microarray data set to further demonstrate the competitiveness and interpretability of our proposed factor regression model.</p>","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"33 1","pages":"27-53"},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10583735/pdf/nihms-1892524.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49684205","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}
{"title":"Empirical Likelihood Using External Summary Information","authors":"Lyu Ni, Junchao Shao, Jinyi Wang, Lei Wang","doi":"10.5705/ss.202023.0056","DOIUrl":"https://doi.org/10.5705/ss.202023.0056","url":null,"abstract":": Statistical analysis in modern scientific research nowadays has opportunities to utilize external summary information from similar studies to gain efficiency. However, the population generating data for current study, referred to as internal population, is typically different from the external population for summary information, although they share some common characteristics that make efficiency improvement possible. The existing population heterogeneity is a challenging issue especially when we have only summary statistics but not individual-level external data. In this paper, we apply an empirical likelihood approach to estimating internal population distribution, with external summary information utilized as constraints for efficiency gain under population heterogeneity. We show that our approach produces an asymptotically more efficient estimator of internal population distribution compared with the customary empirical likelihood without using any external information, under the condition that the external information is based on a dataset with size larger than that","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70939888","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}
Yijian Huang, Isaac Parakati, Dattatraya H Patil, Martin G Sanda
{"title":"Interval estimation for operating characteristic of continuous biomarkers with controlled sensitivity or specificity.","authors":"Yijian Huang, Isaac Parakati, Dattatraya H Patil, Martin G Sanda","doi":"10.5705/ss.202021.0020","DOIUrl":"10.5705/ss.202021.0020","url":null,"abstract":"<p><p>The receiver operating characteristic (ROC) curve provides a comprehensive performance assessment of a continuous biomarker over the full threshold spectrum. Nevertheless, a medical test often dictates to operate at a certain high level of sensitivity or specificity. A diagnostic accuracy metric directly targeting the clinical utility is specificity at the controlled sensitivity level, or vice versa. While the empirical point estimation is readily adopted in practice, the nonparametric interval estimation is challenged by the fact that the variance involves density functions due to estimated threshold. In addition, even with a fixed threshold, many standard confidence intervals including the Wald interval for binomial proportion could have erratic behaviors. In this article, we are motivated by the superior performance of the score interval for binomial proportion and propose a novel extension for the biomarker problem. Meanwhile, we develop exact bootstrap and establish consistency of the bootstrap variance estimator. Both single-biomarker evaluation and two-biomarker comparison are investigated. Extensive simulation studies were conducted, demonstrating competitive performance of our proposals. An illustration with aggressive prostate cancer diagnosis is provided.</p>","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"33 1","pages":"193-214"},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10181819/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9485519","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}
{"title":"High-Dimensional Behaviour of Some Two-Sample Tests Based on Ball Divergence","authors":"Bilol Banerjee, A. Ghosh","doi":"10.5705/ss.202023.0069","DOIUrl":"https://doi.org/10.5705/ss.202023.0069","url":null,"abstract":"","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70939954","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}