BiometrikaPub Date : 2023-12-22DOI: 10.1093/biomet/asad080
P A Maugis
{"title":"Central limit theorems for local network statistics","authors":"P A Maugis","doi":"10.1093/biomet/asad080","DOIUrl":"https://doi.org/10.1093/biomet/asad080","url":null,"abstract":"Summary Subgraph counts, in particular the number of occurrences of small shapes such as triangles, characterize properties of random networks. As a result, they have seen wide use as network summary statistics. Subgraphs are typically counted globally, making existing approaches unable to describe vertex-specific characteristics. In contrast, rooted subgraphs focus on vertex neighbourhoods, and are fundamental descriptors of local network properties. We derive the asymptotic joint distribution of rooted subgraph counts in inhomogeneous random graphs, a model which generalizes most statistical network models. This result enables a shift in the statistical analysis of graphs, from estimating network summaries, to estimating models linking local network structure and vertex-specific covariates. As an example, we consider a school friendship network and show that gender and race are significant predictors of local friendship patterns.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"178 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139051073","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 : 2023-12-21DOI: 10.1093/biomet/asad079
Alexander Aue, Claudia Kirch
{"title":"The state of cumulative sum sequential change point testing seventy years after Page","authors":"Alexander Aue, Claudia Kirch","doi":"10.1093/biomet/asad079","DOIUrl":"https://doi.org/10.1093/biomet/asad079","url":null,"abstract":"\u0000 Quality control charts aim at raising an alarm as soon as sequentially obtained observations of an underlying random process no longer seem to be within stochastic fluctuations prescribed by an ‘in-control’ scenario. Such random processes can often be modelled using the concept of stationarity, or even independence as in most classical works. An important out-of-control scenario is the changepoint alternative, for which the distribution of the process changes at an unknown point in time. In his seminal 1954 Biometrika paper, E. S. Page introduced the famous cumulative sum control charts for changepoint monitoring. Innovatively, decision rules based on cumulative sum procedures took the full history of the process into account, whereas previous procedures were based only on a fixed and typically small number of the most recent observations. The extreme case of using only the most recent observation, often referred to as the Shewhart chart, is more akin to serial outlier than changepoint detection. Page’s cumulative sum approach, introduced seven decades ago, is ubiquitous in modern changepoint analysis, and his original paper has led to a multitude of follow-up papers in different research communities. This review is focused on a particular subfield of this research, namely nonparametric sequential, or online, changepoint tests which are constructed to maintain a desired Type 1 error as opposed to the more traditional approach seeking to minimize the average run length of the procedures. Such tests have originated at the intersection of econometrics and statistics. We trace the development of these tests and highlight their properties, mostly using a simple location model for clarity of exposition, but also review more complex situations such as regression and time series models.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"12 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138951837","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 : 2023-12-20DOI: 10.1093/biomet/asad077
{"title":"Correction to: ‘A cross-validation-based statistical theory for point processes’","authors":"","doi":"10.1093/biomet/asad077","DOIUrl":"https://doi.org/10.1093/biomet/asad077","url":null,"abstract":"","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"45 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139169267","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 : 2023-12-01DOI: 10.1093/biomet/asad075
Shulei Wang, Bo Yuan, T Tony Cai, Hongzhe Li
{"title":"Phylogenetic Association Analysis with Conditional Rank Correlation","authors":"Shulei Wang, Bo Yuan, T Tony Cai, Hongzhe Li","doi":"10.1093/biomet/asad075","DOIUrl":"https://doi.org/10.1093/biomet/asad075","url":null,"abstract":"Summary Phylogenetic association analysis plays a crucial role in investigating the correlation between microbial compositions and specific outcomes of interest in microbiome studies. However, existing methods for testing such associations have limitations related to the assumption of a linear association in high-dimensional settings and the handling of confounding effects. Therefore, there is a need for methods capable of characterizing complex associations, including nonmonotonic relationships. This paper introduces a novel phylogenetic association analysis framework and associated tests to address these challenges by employing conditional rank correlation as a measure of association. These tests account for confounders in a fully nonparametric manner, ensuring robustness against outliers and the ability to detect diverse dependencies. The proposed framework aggregates conditional rank correlations for subtrees using a weighted sum and maximum approach to capture both dense and sparse signals. The significance level of the test statistics is determined by calibrating through a nearest neighbour bootstrapping method, which is straightforward to implement and can accommodate additional datasets when available. The practical advantages of the proposed framework are demonstrated through numerical experiments utilizing both simulated and real microbiome datasets.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"15 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508105","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}
{"title":"Conformalized survival analysis with adaptive cutoffs","authors":"Yu Gui, Rohan Hore, Zhimei Ren, Rina Foygel Barber","doi":"10.1093/biomet/asad076","DOIUrl":"https://doi.org/10.1093/biomet/asad076","url":null,"abstract":"Summary This paper introduces an assumption-lean method that constructs valid and efficient lower predictive bounds (LPBs) for survival times with censored data.We build on recent work by Candès et al. (2021), whose approach first subsets the data to discard any data points with early censoring times, and then uses a reweighting technique (namely, weighted conformal inference (Tibshirani et al., 2019)) to correct for the distribution shift introduced by this subsetting procedure. For our new method, instead of constraining to a fixed threshold for the censoring time when subsetting the data, we allow for a covariate-dependent and data-adaptive subsetting step, which is better able to capture the heterogeneity of the censoring mechanism. As a result, our method can lead to LPBs that are less conservative and give more accurate information. We show that in the Type I right-censoring setting, if either of the censoring mechanism or the conditional quantile of survival time is well estimated, our proposed procedure achieves nearly exact marginal coverage, where in the latter case we additionally have approximate conditional coverage. We evaluate the validity and efficiency of our proposed algorithm in numerical experiments, illustrating its advantage when compared with other competing methods. Finally, our method is applied to a real dataset to generate LPBs for users’ active times on a mobile app.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"5 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508131","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 : 2023-11-28DOI: 10.1093/biomet/asad074
Ryan Thompson, Catherine S Forbes, Steven N Maceachern, Mario Peruggia
{"title":"Familial inference: Tests for hypotheses on a family of centres","authors":"Ryan Thompson, Catherine S Forbes, Steven N Maceachern, Mario Peruggia","doi":"10.1093/biomet/asad074","DOIUrl":"https://doi.org/10.1093/biomet/asad074","url":null,"abstract":"Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their centre. Tests that assess statistical hypotheses of centre implicitly assume a specific centre, e.g., the mean or median. Yet, scientific hypotheses do not always specify a particular centre. This ambiguity leaves the possibility for a gap between scientific theory and statistical practice that can lead to rejection of a true null. In the face of replicability crises in many scientific disciplines, significant results of this kind are concerning. Rather than testing a single centre, this paper proposes testing a family of plausible centres, such as that induced by the Huber loss function. Each centre in the family generates a testing problem, and the resulting family of hypotheses constitutes a familial hypothesis. A Bayesian nonparametric procedure is devised to test familial hypotheses, enabled by a novel pathwise optimization routine to fit the Huber family. The favourable properties of the new test are demonstrated theoretically and experimentally. Two examples from psychology serve as real-world case studies.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"9 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508089","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 : 2023-11-24DOI: 10.1093/biomet/asad073
Yu Gu, Donglin Zeng, Gerardo Heiss, D Y Lin
{"title":"Maximum Likelihood Estimation for Semiparametric Regression Models with Interval-Censored Multistate Data","authors":"Yu Gu, Donglin Zeng, Gerardo Heiss, D Y Lin","doi":"10.1093/biomet/asad073","DOIUrl":"https://doi.org/10.1093/biomet/asad073","url":null,"abstract":"Summary Interval-censored multistate data arise in many studies of chronic diseases, where the health status of a subject can be characterized by a finite number of disease states and the transition between any two states is only known to occur over a broad time interval. We relate potentially time-dependent covariates to multistate processes through semiparametric proportional intensity models with random effects. We study nonparametric maximum likelihood estimation under general interval censoring and develop a stable expectation-maximization algorithm. We show that the resulting parameter estimators are consistent and that the finite-dimensional components are asymptotically normal with a covariance matrix that attains the semiparametric efficiency bound and can be consistently estimated through profile likelihood. In addition, we demonstrate through extensive simulation studies that the proposed numerical and inferential procedures perform well in realistic settings. Finally, we provide an application to a major epidemiologic cohort study.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"16 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508104","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 : 2023-11-20DOI: 10.1093/biomet/asad061
J Cape
{"title":"On varimax asymptotics in network models and spectral methods for dimensionality reduction","authors":"J Cape","doi":"10.1093/biomet/asad061","DOIUrl":"https://doi.org/10.1093/biomet/asad061","url":null,"abstract":"Summary Varimax factor rotations, while popular among practitioners in psychology and statistics since being introduced by H.Kaiser, have historically been viewed with skepticism and suspicion by some theoreticians and mathematical statisticians. Now, work by K. Rohe and M. Zeng provides new, fundamental insight: varimax rotations provably perform statistical estimation in certain classes of latent variable models when paired with spectral-based matrix truncations for dimensionality reduction. We build on this new-found understanding of varimax rotations by developing further connections to network analysis and spectral methods rooted in entrywise matrix perturbation analysis. Concretely, this paper establishes the asymptotic multivariate normality of vectors in varimax-transformed Euclidean point clouds that represent low-dimensional node embeddings in certain latent space random graph models. We address related concepts including network sparsity, data denoising, and the role of matrix rank in latent variable parameterizations. Collectively, these findings, at the confluence of classical and contemporary multivariate analysis, reinforce methodology and inference procedures grounded in matrix factorization-based techniques. Numerical examples illustrate our findings and supplement our discussion.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"19 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508101","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 : 2023-11-16DOI: 10.1093/biomet/asad072
Luca Maestrini, Aishwarya Bhaskaran, Matt P Wand
{"title":"Second term improvement to generalised linear mixed model asymptotics","authors":"Luca Maestrini, Aishwarya Bhaskaran, Matt P Wand","doi":"10.1093/biomet/asad072","DOIUrl":"https://doi.org/10.1093/biomet/asad072","url":null,"abstract":"Summary A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If m denotes the number of groups and n is the average within-group sample size then the asymptotic variances have orders m − 1 and (mn)−1, depending on the parameter. We extend this theory to provide explicit forms of the (mn)−1 second terms of the asymptotically harder-to-estimate parameters. Improved accuracy of statistical inference and planning are consequences of our theory.","PeriodicalId":9001,"journal":{"name":"Biometrika","volume":"9 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508088","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}