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Statistical inference for stationary linear models with tapered data 具有锥形数据的平稳线性模型的统计推断
IF 3.3 Q1 STATISTICS & PROBABILITY Pub Date : 2021-01-01 DOI: 10.1214/21-ss134
M. Ginovyan, A. A. Sahakyan
: In this paper, we survey some recent results on statistical infer- ence (parametric and nonparametric statistical estimation, hypotheses testing) about the spectrum of stationary models with tapered data. We also discuss some questions concerning tapered Toeplitz matrices and operators, central limit theorems for tapered Toeplitz type quadratic functionals, and tapered Fej´er-type kernels and singular integrals. These are the main tools for obtaining the corresponding results, and also are of interest in them- selves. The processes considered will be discrete-time and continuous-time Gaussian, linear or L´evy-driven linear processes with memory.
本文综述了近年来关于具有锥形数据的平稳模型谱的统计推断(参数和非参数统计估计、假设检验)的一些研究成果。讨论了关于锥形Toeplitz矩阵和算子、锥形Toeplitz型二次泛函的中心极限定理、锥形Fej′er型核和奇异积分等问题。这些是获得相应结果的主要工具,也是它们本身感兴趣的。考虑的过程将是离散时间和连续时间高斯,线性或L´evy驱动的线性过程。
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引用次数: 0
Flexible, boundary adapted, nonparametric methods for the estimation of univariate piecewise-smooth functions 单变量分段光滑函数估计的柔性、边界自适应非参数方法
IF 3.3 Q1 STATISTICS & PROBABILITY Pub Date : 2020-01-01 DOI: 10.1214/20-ss128
U. Amato, A. Antoniadis, I. Feis
: We present and compare some nonparametric estimation meth- ods (wavelet and/or spline-based) designed to recover a one-dimensional piecewise-smooth regression function in both a fixed equidistant or not equidistant design regression model and a random design model. Wavelet methods are known to be very competitive in terms of denois- ing and compression, due to the simultaneous localization property of a function in time and frequency. However, boundary assumptions, such as periodicity or symmetry, generate bias and artificial wiggles which degrade overall accuracy. Simple methods have been proposed in the literature for reducing the bias at the boundaries. We introduce new ones based on adaptive combinations of two estimators. The underlying idea is to combine a highly accurate method for non-regular functions, e.g., wavelets, with one well behaved at boundaries, e.g., Splines or Local Polynomial. We provide some asymptotic optimal results supporting our approach. All the methods can handle data with a random design. We also sketch some generalization to the multidimensional setting. the performance of the proposed approaches we have an extensive set of simulations on synthetic data. An interesting regression analysis of two real data applications using these procedures unambiguously demonstrates their effectiveness.
我们提出并比较了一些非参数估计方法(小波和/或基于样条的),旨在恢复一维分段平滑回归函数,在固定等距或非等距设计回归模型和随机设计模型中。由于函数在时间和频率上的同时定位特性,小波方法在去噪和压缩方面具有很强的竞争力。然而,边界假设,如周期性或对称性,会产生偏差和人为波动,从而降低整体精度。在文献中已经提出了一些简单的方法来减少边界上的偏差。我们引入了基于两个估计量自适应组合的新估计量。其基本思想是将高度精确的非正则函数方法(如小波)与在边界处表现良好的方法(如样条或局部多项式)相结合。我们给出了一些支持我们方法的渐近最优结果。所有的方法都可以处理随机设计的数据。我们还概述了对多维设置的一些概括。我们对所提出的方法的性能进行了大量的综合数据模拟。对使用这些过程的两个实际数据应用程序进行了有趣的回归分析,明确地证明了它们的有效性。
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引用次数: 1
Can $p$-values be meaningfully interpreted without random sampling? $p$值可以在没有随机抽样的情况下进行有意义的解释吗?
IF 3.3 Q1 STATISTICS & PROBABILITY Pub Date : 2019-08-16 DOI: 10.31235/osf.io/yazr8
N. Hirschauer, Sven Gruener, O. Musshoff, C. Becker, Antje Jantsch
Besides the inferential errors that abound in the interpretation of p-values, the probabilistic pre-conditions (i.e. random sampling or equivalent) for using them at all are not often met by observa-tional studies in the social sciences. This paper systematizes different sampling designs and discusses the restrictive requirements of data collection that are the sine-qua-non for using p-values.
除了在p值的解释中大量存在的推理误差之外,在社会科学的观察性研究中,使用p值的概率前提条件(即随机抽样或等效)通常不满足。本文系统化了不同的抽样设计,并讨论了数据收集的限制性要求,这些要求是使用p值的正弦条件。
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引用次数: 23
Additive monotone regression in high and lower dimensions 高维和低维的加性单调回归
IF 3.3 Q1 STATISTICS & PROBABILITY Pub Date : 2019-01-01 DOI: 10.1214/19-SS124
S. Engebretsen, I. Glad
In numerous problems where the aim is to estimate the effect of a predictor variable on a response, one can assume a monotone relationship. For example, dose-effect models in medicine are of this type. In a multiple regression setting, additive monotone regression models assume that each predictor has a monotone effect on the response. In this paper, we present an overview and comparison of very recent frequentist methods for fitting additive monotone regression models. Three of the methods we present can be used both in the high dimensional setting, where the number of parameters p exceeds the number of observations n, and in the classical multiple setting where 1 < p ≤ n. However, many of the most recent methods only apply to the classical setting. The methods are compared through simulation experiments in terms of efficiency, prediction error and variable selection properties in both settings, and they are applied to the Boston housing data. We conclude with some recommendations on when the various methods perform best. MSC 2010 subject classifications: Primary 62G08.
在许多以估计预测变量对响应的影响为目的的问题中,人们可以假设一个单调关系。例如,医学中的剂量效应模型就是这种类型。在多元回归设置中,加性单调回归模型假设每个预测器对响应具有单调效应。在本文中,我们提出了一个概述和比较最近的频率方法拟合加性单调回归模型。我们提出的三种方法既可以用于高维设置,其中参数数p超过观测数n,也可以用于经典多重设置,其中1 < p≤n。然而,许多最新的方法仅适用于经典设置。通过仿真实验,比较了两种方法在两种情况下的效率、预测误差和变量选择特性,并将其应用于波士顿住宅数据。最后,我们就各种方法何时表现最佳给出了一些建议。MSC 2010学科分类:初级62G08。
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引用次数: 2
Scalar-on-function regression for predicting distal outcomes from intensively gathered longitudinal data: Interpretability for applied scientists. 从密集收集的纵向数据预测远端结果的标量函数回归:应用科学家的可解释性。
IF 11 Q1 STATISTICS & PROBABILITY Pub Date : 2019-01-01 Epub Date: 2019-11-06 DOI: 10.1214/19-SS126
John J Dziak, Donna L Coffman, Matthew Reimherr, Justin Petrovich, Runze Li, Saul Shiffman, Mariya P Shiyko

Researchers are sometimes interested in predicting a distal or external outcome (such as smoking cessation at follow-up) from the trajectory of an intensively recorded longitudinal variable (such as urge to smoke). This can be done in a semiparametric way via scalar-on-function regression. However, the resulting fitted coefficient regression function requires special care for correct interpretation, as it represents the joint relationship of time points to the outcome, rather than a marginal or cross-sectional relationship. We provide practical guidelines, based on experience with scientific applications, for helping practitioners interpret their results and illustrate these ideas using data from a smoking cessation study.

研究人员有时对根据密集记录的纵向变量(如吸烟冲动)的轨迹预测远端或外部结果(如随访时戒烟)感兴趣。这可以通过函数上的标量回归以半参数的方式实现。然而,所得到的拟合系数回归函数需要特别注意正确的解释,因为它代表了时间点与结果的联合关系,而不是边际或横截面关系。我们提供了基于科学应用经验的实用指南,帮助从业者解释他们的结果,并使用戒烟研究的数据来说明这些想法。
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引用次数: 0
PLS for Big Data: A unified parallel algorithm for regularised group PLS 面向大数据的PLS:正则化群PLS的统一并行算法
IF 3.3 Q1 STATISTICS & PROBABILITY Pub Date : 2019-01-01 DOI: 10.1214/19-ss125
P. L. D. Micheaux, B. Liquet, Matthew Sutton
Partial Least Squares (PLS) methods have been heavily exploited to analyse the association between two blocks of data. These powerful approaches can be applied to data sets where the number of variables is greater than the number of observations and in the presence of high collinearity between variables. Different sparse versions of PLS have been developed to integrate multiple data sets while simultaneously selecting the contributing variables. Sparse modeling is a key factor in obtaining better estimators and identifying associations between multiple data sets. The cornerstone of the sparse PLS methods is the link between the singular value decomposition (SVD) of a matrix (constructed from deflated versions of the original data) and least squares minimization in linear regression. We review four popular PLS methods for two blocks of data. A unified algorithm is proposed to perform all four types of PLS including their regularised versions. We present various approaches to decrease the computation time and show how the whole procedure can be scalable to big data sets. The bigsgPLS R package implements our unified algorithm and is available at https://github.com/matt-sutton/bigsgPLS. MSC 2010 subject classifications: Primary 6202, 62J99.
偏最小二乘(PLS)方法已被大量利用来分析两个数据块之间的关联。这些强大的方法可以应用于变量数量大于观测数量以及变量之间存在高共线性的数据集。不同的稀疏版本的PLS已经开发集成多个数据集,同时选择贡献变量。稀疏建模是获得更好的估计器和识别多个数据集之间关联的关键因素。稀疏PLS方法的基础是矩阵的奇异值分解(SVD)(由原始数据的压缩版本构造)和线性回归中的最小二乘最小化之间的联系。我们回顾了两个数据块的四种流行的PLS方法。提出了一种统一的算法来执行所有四种类型的PLS,包括它们的正则化版本。我们提出了各种方法来减少计算时间,并展示了整个过程如何可扩展到大数据集。bigsgPLS R包实现了我们的统一算法,可在https://github.com/matt-sutton/bigsgPLS获得。MSC 2010学科分类:Primary 6202, 62J99。
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引用次数: 6
Halfspace depth and floating body 半空间深度和浮体
IF 3.3 Q1 STATISTICS & PROBABILITY Pub Date : 2018-09-28 DOI: 10.1214/19-SS123
Stanislav Nagy, C. Schuett, E. Werner
Little known relations of the renown concept of the halfspace depth for multivariate data with notions from convex and affine geometry are discussed. Halfspace depth may be regarded as a measure of symmetry for random vectors. As such, the depth stands as a generalization of a measure of symmetry for convex sets, well studied in geometry. Under a mild assumption, the upper level sets of the halfspace depth coincide with the convex floating bodies used in the definition of the affine surface area for convex bodies in Euclidean spaces. These connections enable us to partially resolve some persistent open problems regarding theoretical properties of the depth.
用凸几何和仿射几何的概念讨论了多元数据的半空间深度这一著名概念中鲜为人知的关系。半空间深度可以看作是随机向量对称性的度量。因此,深度代表了凸集对称度量的泛化,在几何中得到了很好的研究。在温和的假设下,半空间深度的上水平集与欧几里德空间中凸体仿射表面积定义中使用的凸浮体重合。这些联系使我们能够部分地解决一些关于深度理论性质的长期悬而未决的问题。
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引用次数: 34
A design-sensitive approach to fitting regression models with complex survey data 复杂调查数据回归模型拟合的设计敏感方法
IF 3.3 Q1 STATISTICS & PROBABILITY Pub Date : 2018-01-16 DOI: 10.1214/17-SS118
P. Kott
: Fitting complex survey data to regression equations is explored under a design-sensitive model-based framework. A robust version of the standard model assumes that the expected value of the difference between the dependent variable and its model-based prediction is zero no matter what the values of the explanatory variables. The extended model assumes only that the difference is uncorrelated with the covariates. Little is assumed about the error structure of this difference under either model other than independence across primary sampling units. The standard model often fails in practice, but the extended model very rarely does. Under this framework some of the methods developed in the conventional design-based, pseudo-maximum-likelihood framework, such as fitting weighted estimating equations and sandwich mean-squared-error estimation, are retained but their interpretations change. Few of the ideas here are new to the refereed literature. The goal instead is to collect those ideas and put them into a unified conceptual framework. regression models. We will explore an alternative model-based framework for estimating regression models introduced in Kott (2007) that is
在基于设计敏感模型的框架下,探讨了复杂调查数据与回归方程的拟合。标准模型的健壮版本假设,无论解释变量的值是多少,因变量与其基于模型的预测之间的差的期望值都为零。扩展模型仅假设差异与协变量不相关。除了主要采样单元之间的独立性外,两种模型下对这种差异的误差结构几乎没有假设。标准模型在实践中经常失败,但扩展模型很少失败。在这个框架下,传统的基于设计的伪最大似然框架中发展起来的一些方法,如拟合加权估计方程和夹心均方误差估计,被保留了下来,但它们的解释发生了变化。这里的观点对文献来说几乎没有什么新意。相反,我们的目标是收集这些想法,并将它们放入一个统一的概念框架中。回归模型。我们将探索另一种基于模型的框架,用于估计Kott(2007)中引入的回归模型,即
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引用次数: 5
A review of dynamic network models with latent variables. 具有潜在变量的动态网络模型综述。
IF 3.3 Q1 STATISTICS & PROBABILITY Pub Date : 2018-01-01 Epub Date: 2018-09-03 DOI: 10.1214/18-SS121
Bomin Kim, Kevin H Lee, Lingzhou Xue, Xiaoyue Niu

We present a selective review of statistical modeling of dynamic networks. We focus on models with latent variables, specifically, the latent space models and the latent class models (or stochastic blockmodels), which investigate both the observed features and the unobserved structure of networks. We begin with an overview of the static models, and then we introduce the dynamic extensions. For each dynamic model, we also discuss its applications that have been studied in the literature, with the data source listed in Appendix. Based on the review, we summarize a list of open problems and challenges in dynamic network modeling with latent variables.

我们对动态网络的统计建模进行了选择性的回顾。我们关注具有潜在变量的模型,特别是潜在空间模型和潜在类模型(或随机块模型),它们研究网络的观测特征和未观测结构。我们首先概述静态模型,然后介绍动态扩展。对于每个动态模型,我们还讨论了文献中研究的其应用,数据源列于附录中。在综述的基础上,我们总结了具有潜在变量的动态网络建模中的一些悬而未决的问题和挑战。
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引用次数: 106
Pitfalls of significance testing and $p$-value variability: An econometrics perspective 显著性检验和p值变异性的陷阱:计量经济学视角
IF 3.3 Q1 STATISTICS & PROBABILITY Pub Date : 2018-01-01 DOI: 10.1214/18-SS122
N. Hirschauer, Sven Grüner, O. Musshoff, C. Becker
Data on how many scientific findings are reproducible are generally bleak and a wealth of papers have warned against misuses of the p-value and resulting false findings in recent years. This paper discusses the question of what we can(not) learn from the p-value, which is still widely considered as the gold standard of statistical validity. We aim to provide a non-technical and easily accessible resource for statistical practitioners who wish to spot and avoid misinterpretations and misuses of statistical significance tests. For this purpose, we first classify and describe the most widely discussed (“classical”) pitfalls of significance testing, and review published work on these misuses with a focus on regression-based “confirmatory” study. This includes a description of the single-study bias and a simulation-based illustration of how proper meta-analysis compares to misleading significance counts (“vote counting”). Going beyond the classical pitfalls, we also use simulation to provide intuition that relying on the statistical estimate “p-value” as a measure of evidence without considering its sample-to-sample variability falls short of the mark even within an otherwise appropriate interpretation. We conclude with a discussion of the
关于有多少科学发现是可重复的数据通常是黯淡的,近年来,大量的论文警告人们不要滥用p值,从而导致错误的发现。本文讨论了我们能从p值中学到什么(不能)的问题,p值仍然被广泛认为是统计效度的金标准。我们的目标是为希望发现和避免误解和误用统计显著性检验的统计从业人员提供一个非技术和易于获取的资源。为此,我们首先对最广泛讨论的(“经典”)显著性检验陷阱进行分类和描述,并回顾关于这些误用的已发表的工作,重点关注基于回归的“验证性”研究。这包括对单一研究偏差的描述和基于模拟的说明,说明如何将适当的元分析与误导性的显著性计数(“计票”)进行比较。除了经典的陷阱之外,我们还使用模拟来提供直觉,即依赖于统计估计“p值”作为证据的度量,而不考虑其样本间的可变性,即使在其他适当的解释中也达不到要求。最后,我们将讨论
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引用次数: 10
期刊
Statistics Surveys
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