Biometrika最新文献_第5页

Projective Independence Tests in High Dimensions: the Curses and the Cures 高维投射独立性检验:弊与弊

IF 2.7 2区数学

Biometrika Pub Date : 2023-11-15 DOI: 10.1093/biomet/asad070

Yaowu Zhang, Liping Zhu

{"title":"Projective Independence Tests in High Dimensions: the Curses and the Cures","authors":"Yaowu Zhang, Liping Zhu","doi":"10.1093/biomet/asad070","DOIUrl":"https://doi.org/10.1093/biomet/asad070","url":null,"abstract":"Summary Testing independence between high dimensional random vectors is fundamentally different from testing independence between univariate random variables. Take the projection correlation as an example. It suffers from at least three issues. First, it has a high computational complexity of O{n3 (p + q)}, where n, p and q are the respective sample size and dimensions of the random vectors. This limits its usefulness substantially when n is extremely large. Second, the asymptotic null distribution of the projection correlation test is rarely tractable. Therefore, random permutations are often suggested to approximate the asymptotic null distribution. This further increases the complexity of implementing independence tests. Last, the power performance of the projection correlation test deteriorates in high dimensions. To address these issues, we improve the projection correlation through a modified weight function, which reduces the complexity to O{n2 (p + q)}. We estimate the improved projection correlation with U-statistic theory. More importantly, its asymptotic null distribution is standard normal, thanks to the high dimensions of random vectors. This expedites the implementation of independence tests substantially. To enhance power performance in high dimensions, we introduce a cross-validation procedure which incorporates feature screening with the projection correlation test. The implementation efficacy and power enhancement are confirmed through extensive numerical studies.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"11 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 2

Discussion of ‘Statistical inference for streamed longitudinal data’ 关于 "流式纵向数据的统计推断 "的讨论

IF 2.7 2区数学

Biometrika Pub Date : 2023-11-15 DOI: 10.1093/biomet/asad035

J. Wang, H. Wang, K. Chen

引用次数: 0

Discussion of ‘Statistical inference for streamed longitudinal data’ 关于 "流式纵向数据的统计推断 "的讨论

IF 2.7 2区数学

Biometrika Pub Date : 2023-11-15 DOI: 10.1093/biomet/asad034

Peter X-K Song, Ling Zhou

引用次数: 0

Generalized kernel two-sample tests 广义核双样本测试

2区数学

Biometrika Pub Date : 2023-11-14 DOI: 10.1093/biomet/asad068

Hoseung Song, Hao Chen

引用次数: 9

Testing Serial Independence of Object-Valued Time Series 对象值时间序列序列独立性的检验

2区数学

Biometrika Pub Date : 2023-11-11 DOI: 10.1093/biomet/asad069

Feiyu Jiang, Hanjia Gao, Xiaofeng Shao

引用次数: 0

On the optimality of score-driven models 分数驱动模型的最优性

2区数学

Biometrika Pub Date : 2023-11-09 DOI: 10.1093/biomet/asad067

P Gorgi, C S A Lauria, A Luati

{"title":"On the optimality of score-driven models","authors":"P Gorgi, C S A Lauria, A Luati","doi":"10.1093/biomet/asad067","DOIUrl":"https://doi.org/10.1093/biomet/asad067","url":null,"abstract":"Summary Score-driven models have been recently introduced as a general framework to specify time-varying parameters of conditional densities. %The underlying idea is to specify a time-varying parameter as an autoregressive process with innovation given by the score of the associated log-likelihood. The score enjoys stochastic properties that make these models easy to implement and convenient to apply in several contexts, ranging from biostatistics to finance. Score-driven parameter updates have been shown to be optimal in terms of locally reducing a local version of the Kullback–Leibler divergence between the true conditional density and the postulated density of the model. A key limitation of such an optimality property is that it holds only locally both in the parameter space and sample space, yielding to a definition of local Kullback–Leibler divergence that is in fact not a divergence measure. The current paper shows that score-driven updates satisfy stronger optimality properties that are based on a global definition of Kullback–Leibler divergence. In particular, it is shown that score-driven updates reduce the distance between the expected updated parameter and the pseudo-true parameter. Furthermore, depending on the conditional density and the scaling of the score, the optimality result can hold globally over the parameter space, which can be viewed as a generalization of the monotonicity property of the stochastic gradient descent scheme. Several examples illustrate how the results derived in the paper apply to specific models under different easy-to-check assumptions, and provide a formal method to select the link-function and the scaling of the score.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":" 28","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135291655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Graphical tools for selecting conditional instrumental sets 用于选择条件仪表组的图形工具

2区数学

Biometrika Pub Date : 2023-11-03 DOI: 10.1093/biomet/asad066

Henckel, Leonard, Buttenschön, Martin, Maathuis, Marloes H.

{"title":"Graphical tools for selecting conditional instrumental sets","authors":"Henckel, Leonard, Buttenschön, Martin, Maathuis, Marloes H.","doi":"10.1093/biomet/asad066","DOIUrl":"https://doi.org/10.1093/biomet/asad066","url":null,"abstract":"Summary We consider the efficient estimation of total causal effects in the presence of unmeasured confounding using conditional instrumental sets. Specifically, we consider the two-stage least squares estimator in the setting of a linear structural equation model with correlated errors that is compatible with a known acyclic directed mixed graph. To set the stage for our results, we characterize the class of linearly valid conditional instrumental sets that yield consistent two-stage least squares estimators for the target total effect and derive a new asymptotic variance formula for these estimators. Equipped with these results, we provide three graphical tools for selecting more efficient linearly valid conditional instrumental sets. First, a graphical criterion that for certain pairs of linearly valid conditional instrumental sets identifies which of the two corresponding estimators has the smaller asymptotic variance. Second, an algorithm that greedily adds covariates that reduce the asymptotic variance to a given linearly valid conditional instrumental set. Third, a linearly valid conditional instrumental set for which the corresponding estimator has the smallest asymptotic variance that can be ensured with a graphical criterion.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"217 S694","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

On inference in high-dimensional logistic regression models with separated data 分离数据的高维逻辑回归模型的推理

2区数学

Biometrika Pub Date : 2023-11-02 DOI: 10.1093/biomet/asad065

R M Lewis, H S Battey

{"title":"On inference in high-dimensional logistic regression models with separated data","authors":"R M Lewis, H S Battey","doi":"10.1093/biomet/asad065","DOIUrl":"https://doi.org/10.1093/biomet/asad065","url":null,"abstract":"Abstract Direct use of the likelihood function typically produces severely biased estimates when the dimension of the parameter vector is large relative to the effective sample size. With linearly separable data generated from a logistic regression model, the loglikelihood function asymptotes and the maximum likelihood estimator does not exist. We show that an exact analysis for each regression coefficient produces half-infinite confidence sets for some parameters when the data are separable. Such conclusions are not vacuous, but an honest portrayal of the limitations of the data. Finite confidence sets are only achievable when additional, perhaps implicit, assumptions are made. Under a notional double-asymptotic regime in which the dimension of the logistic coefficient vector increases with the sample size, the present paper considers the implications of enforcing a natural constraint on the vector of logistic-transformed probabilities. We derive a relationship between the logistic coefficients and a notional parameter obtained as a probability limit of an ordinary least squares estimator. The latter exists even when the data are separable. Consistency is ascertained under weak conditions on the design matrix.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135975796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Nonparametric priors with full-range borrowing of information 具有全范围信息借用的非参数先验

2区数学

Biometrika Pub Date : 2023-10-19 DOI: 10.1093/biomet/asad063

F Ascolani, B Franzolini, A Lijoi, I Prünster

引用次数: 0

Likelihood-based Inference under Non-Convex Boundary Constraints 非凸边界约束下基于似然的推理

2区数学

Biometrika Pub Date : 2023-10-19 DOI: 10.1093/biomet/asad062

J Y Wang, Z S YE, Y Chen

引用次数: 0