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高维极值图结构学习AI 解读

Extremal graphical models encode the conditional independence structure of multivariate extremes. Key statistics for learning extremal graphical structures are empirical extremal variograms, for which we prove non-asymptotic concentration bounds that hold under general domain of attraction conditions. For the popular class of Hüsler--Reiss models, we propose a majority voting algorithm for learning the underlying graph from data through $L^1$ regularized optimization. Our…

利用方差信息进行面板群组结构的谱聚类估计AI 解读

Consider a panel data setting where repeated observations on individuals are available. Often it is reasonable to assume that there exist groups of individuals that share similar effects of observed characteristics, but the grouping is typically unknown in advance. We first conduct a local analysis which reveals that the variances of the individual coefficient estimates contain useful information for the estimation of group structure. We then propose a method to estimate…

积分 Copula 谱AI 解读

Frequency domain methods form a ubiquitous part of the statistical toolbox for time-series analysis. In recent years, considerable interest has been given to the development of new spectral methodology and tools capturing dynamics in the entire joint distributions, and thus avoiding the limitations of classical, L2-based spectral methods. Most of the spectral concepts proposed in that literature suffer from one major drawback, though: their estimation requires the choice of…

基于自归一化的高维数据变点推断AI 解读

This article considers change-point testing and estimation for a sequence of high-dimensional data. In the case of testing for a mean shift for high-dimensional independent data, we propose a new test which is based on U-statistic in Chen and Qin (Ann. Statist. 38 (2010) 808–835) and utilizes the self-normalization principle (Shao J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 343–366; Shao and Zhang J. Amer. Statist. Assoc. 105 (2010) 1228–1240). Our test targets dense…

渐近依赖与独立下的秩估计及空间极值应用AI 解读

Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the variables is of the same order as observing a large value in all variables simultaneously. However, there is growing evidence that asymptotic independence is equally important in real world applications. Available statistical methodology in the…

多元时间序列极值中的多重块长与重叠分块AI 解读

Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most of the corresponding theory is derived under the simplifying assumption that block maxima are independent observations from a genuine extreme value distribution. In practice, however, block sizes are finite and observations from different blocks are dependent. Theory respecting the latter complications is not well developed, and, in the multivariate case,…

固定效应分位数回归的无偏渐近正态性AI 解读

Nonlinear panel data models with fixed individual effects provide an important set of tools for describing microeconometric data. In a large class of such models (including probit, proportional hazard and quantile regression to name just a few) it is impossible to difference out the individual effects, and inference is usually justified in a ‘large n large T’ asymptotic framework. However, there is a considerable gap in the type of assumptions that are currently imposed in…

通过自标准化检验函数型时间序列的实质性差异AI 解读

Summary We develop methodology for testing relevant hypotheses about functional time series in a tuning-free way. Instead of testing for exact equality, e.g. for the equality of two mean functions from two independent time series, we propose to test the null hypothesis of no relevant deviation. In the two-sample problem this means that an L2-distance between the two mean functions is smaller than a prespecified threshold. For such hypotheses self-normalization, which was…

二元响应模型的平滑分位数回归过程AI 解读

In this article, we consider binary response models with linear quantile restrictions. Considerably generalizing previous research on this topic, our analysis focuses on an infinite collection of quantile estimators. We derive a uniform linearization for the properly standardized empirical quantile process and discover some surprising differences with the setting of continuously observed responses. Moreover, we show that considering quantile processes provides an effective…

含分组固定效应的面板分位数回归AI 解读

This paper introduces estimation methods for grouped latent heterogeneity in panel data quantile regression. We assume that the observed individuals come from a heterogeneous population with a finite number of types. The number of types and group membership is not assumed to be known in advance and is estimated by means of a convex optimization problem. We provide conditions under which group membership is estimated consistently and establish asymptotic normality of the…

分位数回归过程的分布式推断AI 解读

The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big data, we propose a two-step procedure: (i) estimate conditional quantile functions at different levels in a parallel computing environment; (ii) construct a conditional quantile regression process through projection based on these estimated…

混合模型中的同质性检验AI 解读

Statistical models of unobserved heterogeneity are typically formalized as mixtures of simple parametric models and interest naturally focuses on testing for homogeneity versus general mixture alternatives. Many tests of this type can be interpreted as C ( α ) tests, as in Neyman (1959), and shown to be locally asymptotically optimal. These C ( α ) tests will be contrasted with a new approach to likelihood ratio testing for general mixture models. The latter tests are based…

回归曲线的等效性AI 解读

This article investigates the problem whether the difference between two parametric models m1, m2 describing the relation between a response variable and several covariates in two different groups is practically irrelevant, such that inference can be performed on the basis of the pooled sample. Statistical methodology is developed to test the hypotheses H0: d(m1, m2) ⩾ ϵ versus H1: d(m1, m2) < ϵ to demonstrate equivalence between the two regression curves m1, m2 for a…

局部平稳时间序列的分位数谱分析AI 解读

Summary Classical spectral methods are subject to two fundamental limitations: they can account only for covariance-related serial dependences, and they require second-order stationarity. Much attention has been devoted lately to quantile-based spectral methods that go beyond covariance-based serial dependence features. At the same time, covariance-based methods relaxing stationarity into much weaker local stationarity conditions have been developed for a variety of time…

面向海量数据的子抽样双重自助法AI 解读

The bootstrap is a popular and powerful method for assessing precision of estimators and inferential methods. However, for massive datasets that are increasingly prevalent, the bootstrap becomes prohibitively costly in computation and its feasibility is questionable even with modern parallel computing platforms. Recently, Kleiner and co-authors proposed a method called BLB (bag of little bootstraps) for massive data, which is more computationally scalable with little…

一致弱收敛失效时：借助上图与下图研究依赖函数和残差经验过程AI 解读

In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions equipped with the supremum metric. However, there are cases when weak convergence in those spaces fails to hold. Examples include empirical copula and tail dependence processes and residual empirical processes in linear regression models in…

关于基于 Copula 的回归的若干评论AI 解读

In a recent article, Noh, El Ghouch, and Bouezmarni proposed a new semiparametric estimate of a regression function with a multivariate predictor, which is based on a specification of the dependence structure between the predictor and the response by means of a parametric copula. This comment investigates the effect which occurs under misspecification of the parametric model. We demonstrate by means of several examples that even for a one or two-dimensional predictor the…

Pickands 依赖函数的新估计量与极值依赖检验AI 解读

We propose a new class of estimators for Pickands dependence function which is based on the concept of minimum distance estimation. An explicit integral representation of the function A*(t), which minimizes a weighted L2-distance between the logarithm of the copula C(y1−t, yt) and functions of the form A(t)log(y) is derived. If the unknown copula is an extreme-value copula, the function A*(t) coincides with Pickands dependence function. Moreover, even if this is not the…

不交叉分位数曲线的非参数估计AI 解读

Summary Since the introduction by Koenker and Bassett, quantile regression has become increasingly important in many applications. However, many non-parametric conditional quantile estimates yield crossing quantile curves (calculated for various p ∈ (0, 1)). We propose a new non-parametric estimate of conditional quantiles that avoids this problem. The method uses an initial estimate of the conditional distribution function in the first step and solves the problem of…