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Cox processes driven by transformed Gaussian processes on linear networks—A review and new contributions 线性网络上由变换高斯过程驱动的考克斯过程--回顾与新贡献
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2024-05-14 DOI: 10.1111/sjos.12720
Jesper Møller, Jakob G. Rasmussen
{"title":"Cox processes driven by transformed Gaussian processes on linear networks—A review and new contributions","authors":"Jesper Møller, Jakob G. Rasmussen","doi":"10.1111/sjos.12720","DOIUrl":"https://doi.org/10.1111/sjos.12720","url":null,"abstract":"There is a lack of point process models on linear networks. For an arbitrary linear network, we consider new models for a Cox process with an isotropic pair correlation function obtained in various ways by transforming an isotropic Gaussian process which is used for driving the random intensity function of the Cox process. In particular, we introduce three model classes given by log Gaussian, interrupted, and permanental Cox processes on linear networks, and consider for the first time statistical procedures and applications for parametric families of such models. Moreover, we construct new simulation algorithms for Gaussian processes on linear networks and discuss whether the geodesic metric or the resistance metric should be used for the kind of Cox processes studied in this paper.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"209 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141062342","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
On maximizing the likelihood function of general geostatistical models 论一般地质统计模型似然函数的最大化
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2024-05-07 DOI: 10.1111/sjos.12722
Tingjin Chu
{"title":"On maximizing the likelihood function of general geostatistical models","authors":"Tingjin Chu","doi":"10.1111/sjos.12722","DOIUrl":"https://doi.org/10.1111/sjos.12722","url":null,"abstract":"General geostatistical models are powerful tools for analyzing spatial datasets. A two‐step estimation based on the likelihood function is widely used by researchers, but several theoretical and computational challenges remain to be addressed. First, it is unclear whether there is a unique global maximizer of the log‐likelihood function, a seemingly simple but theoretically challenging question. The second challenge is the convexity of the log‐likelihood function. Besides these two challenges in maximizing the likelihood function, we also study the theoretical property of the two‐step estimation. Unlike many previous works, our results can apply to the non‐twice differentiable covariance functions. In the simulation studies, three optimization algorithms are evaluated in terms of maximizing the log‐likelihood functions.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"2016 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140942490","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
Mahalanobis balancing: A multivariate perspective on approximate covariate balancing 马哈拉诺比斯平衡：近似协变量平衡的多变量视角
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2024-04-26 DOI: 10.1111/sjos.12721
Yimin Dai, Ying Yan
{"title":"Mahalanobis balancing: A multivariate perspective on approximate covariate balancing","authors":"Yimin Dai, Ying Yan","doi":"10.1111/sjos.12721","DOIUrl":"https://doi.org/10.1111/sjos.12721","url":null,"abstract":"In the past decade, various exact balancing‐based weighting methods were introduced to the causal inference literature. It eliminates covariate imbalance by imposing balancing constraints in a certain optimization problem, which can nevertheless be infeasible when there is bad overlap between the covariate distributions in the treated and control groups or when the covariates are high dimensional. Recently, approximate balancing was proposed as an alternative balancing framework. It resolves the feasibility issue by using inequality moment constraints instead. However, it can be difficult to select the threshold parameters. Moreover, moment constraints may not fully capture the discrepancy of covariate distributions. In this paper, we propose Mahalanobis balancing to approximately balance covariate distributions from a multivariate perspective. We use a quadratic constraint to control overall imbalance with a single threshold parameter, which can be tuned by a simple selection procedure. We show that the dual problem of Mahalanobis balancing is an norm‐based regularized regression problem, and establish interesting connection to propensity score models. We derive asymptotic properties, discuss the high‐dimensional scenario, and make extensive numerical comparisons with existing balancing methods.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"36 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140801664","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
Asymptotic properties of resampling‐based processes for the average treatment effect in observational studies with competing risks 具有竞争风险的观察性研究中基于重采样过程的平均治疗效果的渐近特性
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2024-04-25 DOI: 10.1111/sjos.12714
Jasmin Rühl, Sarah Friedrich
{"title":"Asymptotic properties of resampling‐based processes for the average treatment effect in observational studies with competing risks","authors":"Jasmin Rühl, Sarah Friedrich","doi":"10.1111/sjos.12714","DOIUrl":"https://doi.org/10.1111/sjos.12714","url":null,"abstract":"In observational studies with time‐to‐event outcomes, the g‐formula can be used to estimate a treatment effect in the presence of confounding factors. However, the asymptotic distribution of the corresponding stochastic process is complicated and thus not suitable for deriving confidence intervals or time‐simultaneous confidence bands for the average treatment effect. A common remedy are resampling‐based approximations, with Efron's nonparametric bootstrap being the standard tool in practice. We investigate the large sample properties of three different resampling approaches and prove their asymptotic validity in a setting with time‐to‐event data subject to competing risks. The usage of these approaches is demonstrated by an analysis of the effect of physical activity on the risk of knee replacement among patients with advanced knee osteoarthritis.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"105 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140801709","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
Minimax estimation of functional principal components from noisy discretized functional data 从噪声离散函数数据中最小估计函数主成分
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2024-04-24 DOI: 10.1111/sjos.12719
Ryad Belhakem, Franck Picard, Vincent Rivoirard, Angelina Roche
{"title":"Minimax estimation of functional principal components from noisy discretized functional data","authors":"Ryad Belhakem, Franck Picard, Vincent Rivoirard, Angelina Roche","doi":"10.1111/sjos.12719","DOIUrl":"https://doi.org/10.1111/sjos.12719","url":null,"abstract":"Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise. However, functional data are noisy and necessarily observed on a finite discretization grid. Common practice consists in smoothing the data and then to compute the functional estimates, but the impact of this denoising step on the procedure's statistical performance are rarely considered. Here we prove new convergence rates for functional principal component estimators. We introduce a double asymptotic framework: one corresponding to the sampling size and a second to the size of the grid. We prove that estimates based on projection onto histograms show optimal rates in a minimax sense. Theoretical results are illustrated on simulated data and the method is applied to the visualization of genomic data.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"101 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140801711","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
A two‐step estimation procedure for semiparametric mixture cure models 半参数混合治愈模型的两步估计程序
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2024-04-19 DOI: 10.1111/sjos.12713
Eni Musta, Valentin Patilea, Ingrid Van Keilegom
{"title":"A two‐step estimation procedure for semiparametric mixture cure models","authors":"Eni Musta, Valentin Patilea, Ingrid Van Keilegom","doi":"10.1111/sjos.12713","DOIUrl":"https://doi.org/10.1111/sjos.12713","url":null,"abstract":"In survival analysis, cure models have been developed to account for the presence of cured subjects that will never experience the event of interest. Mixture cure models with a parametric model for the incidence and a semiparametric model for the survival of the susceptibles are particularly common in practice. Because of the latent cure status, maximum likelihood estimation is performed via the iterative EM algorithm. Here, we focus on the cure probabilities and propose a two‐step procedure to improve upon the maximum likelihood estimator when the sample size is not large. The new method is based on presmoothing by first constructing a nonparametric estimator and then projecting it on the desired parametric class. We investigate the theoretical properties of the resulting estimator and show through an extensive simulation study for the logistic‐Cox model that it outperforms the existing method. Practical use of the method is illustrated through two melanoma datasets.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"87 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140624872","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
Martingale posterior distributions for cumulative hazard functions 累积危害函数的马丁格尔后验分布
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2024-04-07 DOI: 10.1111/sjos.12712
Stephen G. Walker
{"title":"Martingale posterior distributions for cumulative hazard functions","authors":"Stephen G. Walker","doi":"10.1111/sjos.12712","DOIUrl":"https://doi.org/10.1111/sjos.12712","url":null,"abstract":"This paper is about the modeling of cumulative hazard functions using martingale posterior distributions. The focus is on uncertainty quantification from a nonparametric perspective. The foundational Bayesian model in this case is the beta process and the classic estimator is the Nelson–Aalen. We use a sequence of estimators which form a martingale in order to obtain a random cumulative hazard function from the martingale posterior. The connection with the beta process is established and a number of illustrations is presented.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"8 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591815","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
On a computable Skorokhod's integral‐based estimator of the drift parameter in fractional SDE 关于分数 SDE 中漂移参数的可计算斯科罗霍德积分估计器
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2024-03-23 DOI: 10.1111/sjos.12711
Nicolas Marie
{"title":"On a computable Skorokhod's integral‐based estimator of the drift parameter in fractional SDE","authors":"Nicolas Marie","doi":"10.1111/sjos.12711","DOIUrl":"https://doi.org/10.1111/sjos.12711","url":null,"abstract":"This paper deals with a Skorokhod's integral‐based least squares‐ (LS) type estimator of the drift parameter computed from multiple (possibly dependent) copies of the solution of a stochastic differential equation (SDE) driven by a fractional Brownian motion of Hurst index . On the one hand, some convergence results are established on our LS estimator when . On the other hand, when , Skorokhod's integral‐based estimators cannot be computed from data, but in this paper some convergence results are established on a computable approximation of our LS estimator.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"124 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197324","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
Statistical inference for generative adversarial networks and other minimax problems 生成式对抗网络和其他最小问题的统计推理
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2024-03-21 DOI: 10.1111/sjos.12710
Mika Meitz
{"title":"Statistical inference for generative adversarial networks and other minimax problems","authors":"Mika Meitz","doi":"10.1111/sjos.12710","DOIUrl":"https://doi.org/10.1111/sjos.12710","url":null,"abstract":"This paper studies generative adversarial networks (GANs) from the perspective of statistical inference. A GAN is a popular machine learning method in which the parameters of two neural networks, a generator and a discriminator, are estimated to solve a particular minimax problem. This minimax problem typically has a multitude of solutions and the focus of this paper are the statistical properties of these solutions. We address two key statistical issues for the generator and discriminator network parameters, consistent estimation and confidence sets. We first show that the set of solutions to the sample GAN problem is a (Hausdorff) consistent estimator of the set of solutions to the corresponding population GAN problem. We then devise a computationally intensive procedure to form confidence sets and show that these sets contain the population GAN solutions with the desired coverage probability. Small numerical experiments and a Monte Carlo study illustrate our results and verify our theoretical findings. We also show that our results apply in general minimax problems that may be nonconvex, nonconcave, and have multiple solutions.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"15 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197717","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
Efficient drift parameter estimation for ergodic solutions of backward SDEs 后向 SDE 的遍历解的高效漂移参数估计
IF 1 4区 数学
Scandinavian Journal of Statistics Pub Date : 2024-02-27 DOI: 10.1111/sjos.12709
Teppei Ogihara, Mitja Stadje
{"title":"Efficient drift parameter estimation for ergodic solutions of backward SDEs","authors":"Teppei Ogihara, Mitja Stadje","doi":"10.1111/sjos.12709","DOIUrl":"https://doi.org/10.1111/sjos.12709","url":null,"abstract":"We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our analysis is that the stochastic integral part is unobserved and nonparametric. Additionally, the drift may depend on the (unknown and unobserved) stochastic integrand. Our results hold for ergodic semi-parametric diffusions and backward SDEs. Simulation studies confirm that the methods proposed yield good convergence results.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"170 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140001947","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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