BiometrikaPub Date : 2023-04-04DOI: 10.1093/biomet/asad024
Anna Calissano, Aasa Feragen, S. Vantini
{"title":"Populations of Unlabelled Networks: Graph Space Geometry and Generalized Geodesic Principal Components","authors":"Anna Calissano, Aasa Feragen, S. Vantini","doi":"10.1093/biomet/asad024","DOIUrl":"https://doi.org/10.1093/biomet/asad024","url":null,"abstract":"\u0000 Statistical analysis for populations of networks is widely applicable but challenging as networks have strongly non-Euclidean behaviour. Graph space is an exhaustive framework for studying populations of unlabelled networks which are weighted or unweighted, uni- or multi-layered, directed or undirected. Viewing graph space as the quotient of a Euclidean space with respect to a finite group action, we show that it is not a manifold, and that its curvature is unbounded from above. Within this geometrical framework we define generalized geodesic principal components, and we introduce the align all and compute algorithms, all of which allow for the computation of statistics on graph space. The statistics and algorithms are compared with existing methods and empirically validated on three real datasets, showcasing the framework potential utility. The whole framework is implemented within the geomstats Python package.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":" ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48150426","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}
BiometrikaPub Date : 2023-03-23eCollection Date: 2023-01-01DOI: 10.5114/cipp/155945
Mariola Łaguna, Emilia Mielniczuk, Wiktor Razmus
{"title":"Development and initial validation of the Daily Goal Realization Scale.","authors":"Mariola Łaguna, Emilia Mielniczuk, Wiktor Razmus","doi":"10.5114/cipp/155945","DOIUrl":"10.5114/cipp/155945","url":null,"abstract":"<p><strong>Background: </strong>This paper presents the results of three studies allowing the design and initial validation of the Daily Goal Realization Scale (DGRS). Goal realization refers to the engagement in goal-directed behavior that leads to progress in personal goal attainment; it is considered one of the adaptive personal characteristics.</p><p><strong>Participants and procedure: </strong>Three studies, including an initial study to develop and select the items (Study 1), an intensive longitudinal study (Study 2), and a multiple goal evaluation study (Study 3), tested factorial structure, reliability and validity of the measure.</p><p><strong>Results: </strong>Multilevel confirmatory factor analysis confirmed the unidimensional structure of the DGRS (obtained in Study 1) both at the individual and goal level, captured as daily goal realization (Study 2) and as multiple goal realization (Study 3). The validity of the DGRS was supported by meaningful associations with other goal evaluations (Study 3). As expected, the DGRS was positively related to evaluations of progress in goal achievement, engagement, likelihood of success, and goal importance. The DGRS also demonstrated measurement invariance allowing for meaningful comparisons of scores between men and women.</p><p><strong>Conclusions: </strong>The findings indicate that the DGRS is a brief and reliable idiographic measure of daily goal realization. The scale has excellent internal consistency and good criterion validity.</p>","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"51 1","pages":"240-250"},"PeriodicalIF":1.0,"publicationDate":"2023-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10654345/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82684058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
BiometrikaPub Date : 2023-03-21DOI: 10.1093/biomet/asad021
Dimitris N Politis
{"title":"Scalable subsampling: computation, aggregation and inference","authors":"Dimitris N Politis","doi":"10.1093/biomet/asad021","DOIUrl":"https://doi.org/10.1093/biomet/asad021","url":null,"abstract":"Abstract Subsampling has seen a resurgence in the big data era where the standard, full-resample size bootstrap can be infeasible to compute. Nevertheless, even choosing a single random subsample of size b can be computationally challenging with both b and the sample size n being very large. This paper shows how a set of appropriately chosen, nonrandom subsamples can be used to conduct effective, and computationally feasible, subsampling distribution estimation. Furthermore, the same set of subsamples can be used to yield a procedure for subsampling aggregation, also known as subagging, that is scalable with big data. Interestingly, the scalable subagging estimator can be tuned to have the same, or better, rate of convergence than that of θ^n. Statistical inference could then be based on the scalable subagging estimator instead of the original θ^n.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"438 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135001298","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}
BiometrikaPub Date : 2023-03-16DOI: 10.1093/biomet/asad019
F. Sävje
{"title":"Causal inference with misspecified exposure mappings: separating definitions and assumptions","authors":"F. Sävje","doi":"10.1093/biomet/asad019","DOIUrl":"https://doi.org/10.1093/biomet/asad019","url":null,"abstract":"\u0000 Exposure mappings facilitate investigations of complex causal effects when units interact in experiments. Current methods require experimenters to use the same exposure mappings both to define the effect of interest and to impose assumptions on the interference structure. However, the two roles rarely coincide in practice, and experimenters are forced to make the often questionable assumption that their exposures are correctly specified. This paper argues that the two roles exposure mappings currently serve can, and typically should, be separated, so that exposures are used to define effects without necessarily assuming that they are capturing the complete causal structure in the experiment. The paper shows that this approach is practically viable by providing conditions under which exposure effects can be precisely estimated when the exposures are misspecified. Some important questions remain open.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":" ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49317373","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}
BiometrikaPub Date : 2023-03-15DOI: 10.1093/biomet/asad018
Giovanni Motta, W. Wu, M. Pourahmadi
{"title":"√2-Estimation for Smooth Eigenvectors of Matrix-Valued Functions","authors":"Giovanni Motta, W. Wu, M. Pourahmadi","doi":"10.1093/biomet/asad018","DOIUrl":"https://doi.org/10.1093/biomet/asad018","url":null,"abstract":"\u0000 Modern statistical methods for multivariate time series rely on the eigendecomposition of matrix-valued functions such as time-varying covariance and spectral density matrices. The curse of indeterminacy or misidentification of smooth eigenvector functions has not received much attention. We resolve this important problem and recover smooth trajectories by examining the distance between the eigenvectors of the same matrix-valued function evaluated at two consecutive points. We change the sign of the next eigenvector if its distance with the current one is larger than the square root of 2. In the case of distinct eigenvalues, this simple method delivers smooth eigenvectors. For coalescing eigenvalues, we match the corresponding eigenvectors and apply an additional signing around the coalescing points. We establish consistency and rates of convergence for the proposed smooth eigenvector estimators. Simulation results and applications to real data confirm that our approach is needed to obtain smooth eigenvectors.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":" ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42009018","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}
BiometrikaPub Date : 2023-03-01Epub Date: 2022-04-05DOI: 10.1093/biomet/asac021
Jinsong Chen, Quefeng Li, Hua Yun Chen
{"title":"Testing generalized linear models with high-dimensional nuisance parameter.","authors":"Jinsong Chen, Quefeng Li, Hua Yun Chen","doi":"10.1093/biomet/asac021","DOIUrl":"10.1093/biomet/asac021","url":null,"abstract":"<p><p>Generalized linear models often have a high-dimensional nuisance parameters, as seen in applications such as testing gene-environment interactions or gene-gene interactions. In these scenarios, it is essential to test the significance of a high-dimensional sub-vector of the model's coefficients. Although some existing methods can tackle this problem, they often rely on the bootstrap to approximate the asymptotic distribution of the test statistic, and thus are computationally expensive. Here, we propose a computationally efficient test with a closed-form limiting distribution, which allows the parameter being tested to be either sparse or dense. We show that under certain regularity conditions, the type I error of the proposed method is asymptotically correct, and we establish its power under high-dimensional alternatives. Extensive simulations demonstrate the good performance of the proposed test and its robustness when certain sparsity assumptions are violated. We also apply the proposed method to Chinese famine sample data in order to show its performance when testing the significance of gene-environment interactions.</p>","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"110 1","pages":"83-99"},"PeriodicalIF":2.7,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9933885/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10800040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
BiometrikaPub Date : 2023-02-28DOI: 10.1093/biomet/asad012
S Ward, H S Battey, E A K Cohen
{"title":"Nonparametric estimation of the intensity function of a spatial point process on a Riemannian manifold","authors":"S Ward, H S Battey, E A K Cohen","doi":"10.1093/biomet/asad012","DOIUrl":"https://doi.org/10.1093/biomet/asad012","url":null,"abstract":"Summary This paper is concerned with nonparametric estimation of the intensity function of a point process on a Riemannian manifold. It provides a first-order asymptotic analysis of the proposed kernel estimator for Poisson processes, supplemented by empirical work to probe the behaviour in finite samples and under other generative regimes. The investigation highlights the scope for finite-sample improvements by allowing the bandwidth to adapt to local curvature.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"650 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135827732","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}
BiometrikaPub Date : 2023-02-24DOI: 10.1093/biomet/asad014
A. Mccormack, P. Hoff
{"title":"Equivariant Estimation of Fréchet Means","authors":"A. Mccormack, P. Hoff","doi":"10.1093/biomet/asad014","DOIUrl":"https://doi.org/10.1093/biomet/asad014","url":null,"abstract":"\u0000 The Fréchet mean generalizes the concept of a mean to a metric space setting. In this work we consider equivariant estimation of Fréchet means for parametric models on metric spaces that are Riemannian manifolds. The geometry and symmetry of such a space is partially encoded by its isometry group of distance preserving transformations. Estimators that are equivariant under the isometry group take into account the symmetry of the metric space. For some models there exists an optimal equivariant estimator, which necessarily will perform as well or better than other common equivariant estimators, such as the maximum likelihood estimator or the sample Fréchet mean. We derive the general form of this minimum risk equivariant estimator and in a few cases provide explicit expressions for it. A result for finding the Fréchet mean for distributions with radially decreasing densities is presented and used to find expressions for the minimum risk equivariant estimator. In some models the isometry group is not large enough relative to the parametric family of distributions for there to exist a minimum risk equivariant estimator. In such cases, we introduce an adaptive equivariant estimator that uses the data to select a submodel for which there is a minimum risk equivariant estimator. Simulation results show that the adaptive equivariant estimator performs favourably relative to alternative estimators.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"1 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41441805","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}
BiometrikaPub Date : 2023-02-20DOI: 10.1093/biomet/asad010
Lan Luo, Jingshen Wang, Emily C Hector
{"title":"Statistical inference for streamed longitudinal data","authors":"Lan Luo, Jingshen Wang, Emily C Hector","doi":"10.1093/biomet/asad010","DOIUrl":"https://doi.org/10.1093/biomet/asad010","url":null,"abstract":"Summary Modern longitudinal data, for example from wearable devices, may consist of measurements of biological signals on a fixed set of participants at a diverging number of time-points. Traditional statistical methods are not equipped to handle the computational burden of repeatedly analysing the cumulatively growing dataset each time new data are collected. We propose a new estimation and inference framework for dynamic updating of point estimates and their standard errors along sequentially collected datasets with dependence, both within and between the datasets. The key technique is a decomposition of the extended inference function vector of the quadratic inference function constructed over the cumulative longitudinal data into a sum of summary statistics over data batches. We show how this sum can be recursively updated without the need to access the whole dataset, resulting in a computationally efficient streaming procedure with minimal loss of statistical efficiency. We prove consistency and asymptotic normality of our streaming estimator as the number of data batches diverges, even as the number of independent participants remains fixed. Simulations demonstrate the advantages of our approach over traditional statistical methods that assume independence between data batches. Finally, we investigate the relationship between physical activity and several diseases through analysis of accelerometry data from the National Health and Nutrition Examination Survey.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134905480","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}
BiometrikaPub Date : 2023-02-14DOI: 10.1093/biomet/asad009
A J Gutknecht, L Barnett
{"title":"Sampling distribution for single-regression Granger causality estimators","authors":"A J Gutknecht, L Barnett","doi":"10.1093/biomet/asad009","DOIUrl":"https://doi.org/10.1093/biomet/asad009","url":null,"abstract":"Summary The single-regression Granger–Geweke causality estimator has previously been shown to solve known problems associated with the more conventional likelihood ratio estimator; however, its sampling distribution has remained unknown. We show that, under the null hypothesis of vanishing Granger causality, the single-regression estimator converges to a generalized χ2 distribution, which is well approximated by a Γ distribution. We show that this holds too for Geweke’s spectral causality averaged over a given frequency band, and derive explicit expressions for the generalized χ2 and Γ-approximation parameters in both cases. We present a Neyman–Pearson test based on the single-regression estimators, and discuss how it may be deployed in empirical scenarios. We outline how our analysis may be extended to the conditional case, point-frequency spectral Granger causality and the important case of state-space Granger causality.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"518 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135727143","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}