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Robust Inference for High‐Dimensional Single Index Models 高维单指标模型的鲁棒推断
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2023-03-13 DOI: 10.1111/sjos.12638
Dongxiao Han, Miao Han, Jian Huang, Yuanyuan Lin
{"title":"Robust Inference for\u0000 High‐Dimensional\u0000 Single Index Models","authors":"Dongxiao Han, Miao Han, Jian Huang, Yuanyuan Lin","doi":"10.1111/sjos.12638","DOIUrl":"https://doi.org/10.1111/sjos.12638","url":null,"abstract":"We propose a robust inference method for high‐dimensional single index models with an unknown link function and elliptically symmetrically distributed covariates, focusing on signal recovery and inference. The proposed method is built on the Huber loss and the estimation of the unknown link function is avoided. The ℓ1$$ {ell}_1 $$ and ℓ2$$ {ell}_2 $$ consistency of a Lasso estimator up to a multiplicative scalar is established. When the covariance matrix of the predictors satisfies the irrepresentable condition, our method is shown to recover the signed support of the true parameter under mild conditions. Based on a debiased Lasso estimator, we study component‐wise and group inference for the high‐dimensional index parameter. The finite‐sample performance of our method is evaluated through extensive simulation studies. An application to a riboflavin production dataset is provided to illustrate the proposed method.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43396597","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}
引用次数: 0
Remove unwanted variation retrieves unknown experimental designs 去除不需要的变异，检索未知的实验设计
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2023-03-01 DOI: 10.1111/sjos.12633
Ingrid Lönnstedt, T. Speed
{"title":"Remove unwanted variation retrieves unknown experimental designs","authors":"Ingrid Lönnstedt, T. Speed","doi":"10.1111/sjos.12633","DOIUrl":"https://doi.org/10.1111/sjos.12633","url":null,"abstract":"Remove unwanted variation (RUV) is an estimation and normalization system in which the underlying correlation structure of a multivariate dataset is estimated from negative control measurements, typically gene expression values, which are assumed to stay constant across experimental conditions. In this paper we derive the weight matrix which is estimated and incorporated into the generalized least squares estimates of RUV‐inverse, and show that this weight matrix estimates the average covariance matrix across negative control measurements. RUV‐inverse can thus be viewed as an estimation method adjusting for an unknown experimental design. We show that for a balanced incomplete block design (BIBD), RUV‐inverse recovers intra‐ and interblock estimates of the relevant parameters and combines them as a weighted sum just like the best linear unbiased estimator (BLUE), except that the weights are globally estimated from the negative control measurements instead of being individually optimized to each measurement as in the classical, single measurement BIBD BLUE.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"101 - 89"},"PeriodicalIF":1.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42340017","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}
引用次数: 0
Finite sample inference for empirical Bayesian methods 经验贝叶斯方法的有限样本推理
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2023-02-28 DOI: 10.1111/sjos.12643
H. Nguyen, Mayetri Gupta
{"title":"Finite sample inference for empirical Bayesian methods","authors":"H. Nguyen, Mayetri Gupta","doi":"10.1111/sjos.12643","DOIUrl":"https://doi.org/10.1111/sjos.12643","url":null,"abstract":"In recent years, empirical Bayesian (EB) inference has become an attractive approach for estimation in parametric models arising in a variety of real-life problems, especially in complex and high-dimensional scientific applications. However, compared to the relative abundance of available general methods for computing point estimators in the EB framework, the construction of confidence sets and hypothesis tests with good theoretical properties remains difficult and problem specific. Motivated by the universal inference framework of Wasserman et al. (2020), we propose a general and universal method, based on holdout likelihood ratios, and utilizing the hierarchical structure of the specified Bayesian model for constructing confidence sets and hypothesis tests that are finite sample valid. We illustrate our method through a range of numerical studies and real data applications, which demonstrate that the approach is able to generate useful and meaningful inferential statements in the relevant contexts.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44494191","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}
引用次数: 0
Professor Elja Arjas: A prominent figure in establishing statistics in Finland Elja Arjas教授:在芬兰建立统计学的杰出人物
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2023-02-21 DOI: 10.1111/sjos.12631
S. Kulathinal, Jaakko Peltonen, M. Sillanpää
{"title":"Professor Elja Arjas: A prominent figure in establishing statistics in Finland","authors":"S. Kulathinal, Jaakko Peltonen, M. Sillanpää","doi":"10.1111/sjos.12631","DOIUrl":"https://doi.org/10.1111/sjos.12631","url":null,"abstract":"","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48459555","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}
引用次数: 0
Frequentist model averaging for envelope models 包络模型的频域模型平均
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2023-01-27 DOI: 10.1111/sjos.12634
Ziwen Gao, Jiahui Zou, Xinyu Zhang, Yanyuan Ma
{"title":"Frequentist model averaging for envelope models","authors":"Ziwen Gao, Jiahui Zou, Xinyu Zhang, Yanyuan Ma","doi":"10.1111/sjos.12634","DOIUrl":"https://doi.org/10.1111/sjos.12634","url":null,"abstract":"The envelope method produces efficient estimation in multivariate linear regression, and is widely applied in biology, psychology, and economics. This paper estimates parameters through a model averaging methodology and promotes the predicting abilities of the envelope models. We propose a frequentist model averaging method by minimizing a cross‐validation criterion. When all the candidate models are misspecified, the proposed model averaging estimator is proved to be asymptotically optimal. When correct candidate models exist, the coefficient estimator is proved to be consistent, and the sum of the weights assigned to the correct models, in probability, converges to one. Simulations and an empirical application demonstrate the effectiveness of the proposed method.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"1325 - 1364"},"PeriodicalIF":1.0,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45126662","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}
引用次数: 1
Variable selection for high‐dimensional generalized linear model with block‐missing data 具有块缺失数据的高维广义线性模型的变量选择
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2023-01-23 DOI: 10.1111/sjos.12632
Yifan He, Yang Feng, Xinyuan Song
{"title":"Variable selection for high‐dimensional generalized linear model with block‐missing data","authors":"Yifan He, Yang Feng, Xinyuan Song","doi":"10.1111/sjos.12632","DOIUrl":"https://doi.org/10.1111/sjos.12632","url":null,"abstract":"In modern scientific research, multiblock missing data emerges with synthesizing information across multiple studies. However, existing imputation methods for handling block‐wise missing data either focus on the single‐block missing pattern or heavily rely on the model structure. In this study, we propose a single regression‐based imputation algorithm for multiblock missing data. First, we conduct a sparse precision matrix estimation based on the structure of block‐wise missing data. Second, we impute the missing blocks with their means conditional on the observed blocks. Theoretical results about variable selection and estimation consistency are established in the context of a generalized linear model. Moreover, simulation studies show that compared with existing methods, the proposed imputation procedure is robust to various missing mechanisms because of the good properties of regression imputation. An application to Alzheimer's Disease Neuroimaging Initiative data also confirms the superiority of our proposed method.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"1279 - 1297"},"PeriodicalIF":1.0,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43310881","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}
引用次数: 0
Use of multiple imputation in supersampled nested case‐control and case‐cohort studies 在超样本嵌套病例对照和病例队列研究中使用多重输入
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2022-12-20 DOI: 10.1111/sjos.12624
Ørnulf Borgan, R. Keogh, A. Njøs
{"title":"Use of multiple imputation in supersampled nested case‐control and case‐cohort studies","authors":"Ørnulf Borgan, R. Keogh, A. Njøs","doi":"10.1111/sjos.12624","DOIUrl":"https://doi.org/10.1111/sjos.12624","url":null,"abstract":"Nested case‐control and case‐cohort studies are useful for studying associations between covariates and time‐to‐event when some covariates are expensive to measure. Full covariate information is collected in the nested case‐control or case‐cohort sample only, while cheaply measured covariates are often observed for the full cohort. Standard analysis of such case‐control samples ignores any full cohort data. Previous work has shown how data for the full cohort can be used efficiently by multiple imputation of the expensive covariate(s), followed by a full‐cohort analysis. For large cohorts this is computationally expensive or even infeasible. An alternative is to supplement the case‐control samples with additional controls on which cheaply measured covariates are observed. We show how multiple imputation can be used for analysis of such supersampled data. Simulations show that this brings efficiency gains relative to a traditional analysis and that the efficiency loss relative to using the full cohort data is not substantial.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"13 - 37"},"PeriodicalIF":1.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42358767","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}
引用次数: 0
Divergence versus decision P‐values: A distinction worth making in theory and keeping in practice: Or, how divergence P‐values measure evidence even when decision P‐values do not 分歧与决策P值:一个值得在理论和实践中做出的区分;或者，分歧P值如何衡量证据，即使决策P值没有
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2022-12-11 DOI: 10.1111/sjos.12625
S. Greenland
{"title":"Divergence versus decision P‐values: A distinction worth making in theory and keeping in practice: Or, how divergence P‐values measure evidence even when decision P‐values do not","authors":"S. Greenland","doi":"10.1111/sjos.12625","DOIUrl":"https://doi.org/10.1111/sjos.12625","url":null,"abstract":"There are two distinct definitions of “P‐value” for evaluating a proposed hypothesis or model for the process generating an observed dataset. The original definition starts with a measure of the divergence of the dataset from what was expected under the model, such as a sum of squares or a deviance statistic. A P‐value is then the ordinal location of the measure in a reference distribution computed from the model and the data, and is treated as a unit‐scaled index of compatibility between the data and the model. In the other definition, a P‐value is a random variable on the unit interval whose realizations can be compared to a cutoff α to generate a decision rule with known error rates under the model and specific alternatives. It is commonly assumed that realizations of such decision P‐values always correspond to divergence P‐values. But this need not be so: Decision P‐values can violate intuitive single‐sample coherence criteria where divergence P‐values do not. It is thus argued that divergence and decision P‐values should be carefully distinguished in teaching, and that divergence P‐values are the relevant choice when the analysis goal is to summarize evidence rather than implement a decision rule.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"54 - 88"},"PeriodicalIF":1.0,"publicationDate":"2022-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42293279","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}
引用次数: 6
Robust quasi‐randomization‐based estimation with ensemble learning for missing data 缺失数据的基于集成学习的稳健准随机化估计
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2022-12-11 DOI: 10.1111/sjos.12626
Danhyang Lee, Li‐Chun Zhang, Sixia Chen
{"title":"Robust quasi‐randomization‐based estimation with ensemble learning for missing data","authors":"Danhyang Lee, Li‐Chun Zhang, Sixia Chen","doi":"10.1111/sjos.12626","DOIUrl":"https://doi.org/10.1111/sjos.12626","url":null,"abstract":"Missing data analysis requires assumptions about an outcome model or a response probability model to adjust for potential bias due to nonresponse. Doubly robust (DR) estimators are consistent if at least one of the models is correctly specified. Multiply robust (MR) estimators extend DR estimators by allowing for multiple models for both the outcome and/or response probability models and are consistent if at least one of the multiple models is correctly specified. We propose a robust quasi‐randomization‐based model approach to bring more protection against model misspecification than the existing DR and MR estimators, where any multiple semiparametric, nonparametric or machine learning models can be used for the outcome variable. The proposed estimator achieves unbiasedness by using a subsampling Rao–Blackwell method, given cell‐homogenous response, regardless of any working models for the outcome. An unbiased variance estimation formula is proposed, which does not use any replicate jackknife or bootstrap methods. A simulation study shows that our proposed method outperforms the existing multiply robust estimators.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"1263 - 1278"},"PeriodicalIF":1.0,"publicationDate":"2022-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41355945","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}
引用次数: 0
Selection of linear mixed‐effects models for clustered data 聚类数据线性混合效应模型的选择
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2022-12-08 DOI: 10.1111/sjos.12623
Chih‐Hao Chang, Hsin-Cheng Huang, C. Ing
{"title":"Selection of linear mixed‐effects models for clustered data","authors":"Chih‐Hao Chang, Hsin-Cheng Huang, C. Ing","doi":"10.1111/sjos.12623","DOIUrl":"https://doi.org/10.1111/sjos.12623","url":null,"abstract":"We consider model selection for linear mixed‐effects models with clustered structure, where conditional Kullback–Leibler (CKL) loss is applied to measure the efficiency of the selection. We estimate the CKL loss by substituting the empirical best linear unbiased predictors (EBLUPs) into random effects with model parameters estimated by maximum likelihood. Although the BLUP approach is commonly used in predicting random effects and future observations, selecting random effects to achieve asymptotic loss efficiency concerning CKL loss is challenging and has not been well studied. In this paper, we propose addressing this difficulty using a conditional generalized information criterion (CGIC) with two tuning parameters. We further consider a challenging but practically relevant situation where the number, m$$ m $$ , of clusters does not go to infinity with the sample size. Hence the random‐effects variances are not consistently estimable. We show that via a novel decomposition of the CKL risk, the CGIC achieves consistency and asymptotic loss efficiency, whether m$$ m $$ is fixed or increases to infinity with the sample size. We also conduct numerical experiments to illustrate the theoretical findings.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"50 1","pages":"875 - 897"},"PeriodicalIF":1.0,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44731261","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}
引用次数: 0
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