Jelena Bradic, Yinchu Zhu
We provide comments on the article "High-dimensional simultaneous inference with the bootstrap" by Ruben Dezeure, Peter Buhlmann and Cun-Hui Zhang.
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We provide some comments on the article `High-dimensional simultaneous inference with the bootstrap' by Ruben Dezeure, Peter Buhlmann and Cun-Hui Zhang.
Choi and Shin (2020) have constructed a bootstrap-based test for change-points in panels with temporal and and/or cross-sectional dependence. They have compared their test to several other proposed tests. We demonstrate that by an appropriate, data-adaptive choice of the block length, the change-point test by Sharipov, Tewes, Wendler (2016) can at least cope with mild temporal dependence, the size distortion of this test is not as severe as claimed by Choi and Shin (2020).
We propose a residual and wild bootstrap methodology for individual and simultaneous inference in high-dimensional linear models with possibly non-Gaussian and heteroscedastic errors. We establish asymptotic consistency for simultaneous inference for parameters in groups $G$, where $p \gg n$, $s_0 = o(n^{1/2}/\{\log(p) \log(|G|)^{1/2}\})$ and $\log(|G|) = o(n^{1/7})$, with $p$ the number of variables, $n$ the sample size and $s_0$ denoting the sparsity. The theory is complemented by many empirical results. Our proposed procedures are implemented in the R-package hdi.
Comment on "An implementation of neural simulation-based inference for parameter estimation in ATLAS''
评论指出ATLAS论文中用于估计模拟数据集有限性不确定性的双重自助法技术，经玩具示例验证，未能有效捕获该不确定性。
We propose a distributed bootstrap method for simultaneous inference on high-dimensional massive data that are stored and processed with many machines. The method produces an $\ell_\infty$-norm confidence region based on a communication-efficient de-biased lasso, and we propose an efficient cross-validation approach to tune the method at every iteration. We theoretically prove a lower bound on the number of communication rounds $τ_{\min}$ that warrants the statistical accuracy and efficiency. Furthermore, $τ_{\min}$ only increases logarithmically with the number of workers and the intrinsic di…
Simultaneous confidence bands for cumulative hazard via exchangeable bootstrap and box calibration
针对右删失数据中累积风险函数的重抽样置信带覆盖不足问题，提出结合可交换自助法与箱线校准的方法，在保留Nelson-Aalen比结构的同时构建置信带，渐近达到名义覆盖水平。
Robust Sensitivity Analysis via Augmented Percentile Bootstrap under Simultaneous Violations of Unconfoundedness and Overlap
本文提出一种统一且灵活的敏感性分析框架，在放宽无混杂性和重叠性假设的基础上，通过线性规划计算最坏情况界限，并引入增强百分位自助法进行统计推断，以稳健地估计重叠加权平均处理效应。
We propose a new approach to the problem of high-dimensional multivariate ANOVA via bootstrapping max statistics that involve the differences of sample mean vectors. The proposed method proceeds via the construction of simultaneous confidence regions for the differences of population mean vectors. It is suited to simultaneously test the equality of several pairs of mean vectors of potentially more than two populations. By exploiting the variance decay property that is a natural feature in relevant applications, we are able to provide dimension-free and nearly-parametric convergence rates for G…
Simultaneous inference for high-dimensional non-Gaussian time series is always considered to be a challenging problem. Such tasks require not only robust estimation of the coefficients in the random process, but also deriving limiting distribution for a sum of dependent variables. In this paper, we propose a multiplier bootstrap procedure to conduct simultaneous inference for the transition coefficients in high-dimensional non-Gaussian vector autoregressive (VAR) models. This bootstrap-assisted procedure allows the dimension of the time series to grow exponentially fast in the number of observ…
Cluster on the Subject, Not the Record: Confidence Intervals and Simultaneous Bands for Additive-Hazards Sequential Trial Emulation
该研究针对加性风险序贯试验模拟，指出行级稳健方差存在反保守性，提出受试者聚类方差和乘子自助法可改善置信区间覆盖率，并通过模拟和实际数据验证了方法有效性，相关代码已整合至steCI R包。
FDP control in multivariate linear models using the bootstrap
本研究针对多元线性模型中多对比的错误发现比例事后推断问题，结合自助法与现有事后推断界，通过林德伯格中心极限定理证明相合性，实现FDP同时渐近控制，功效优于现有参数方法，并在影像与转录组数据上验证有效。
AR-sieve Bootstrap for High-dimensional Time Series
本文提出一种新的高维时间序列AR-筛bootstrap方法，通过因子建模降低维度并捕捉时间依赖性，建立基于因子的bootstrap流程，并在高维场景中验证其有效性。
In this paper, we develop uniform inference methods for the conditional mode based on quantile regression. Specifically, we propose to estimate the conditional mode by minimizing the derivative of the estimated conditional quantile function defined by smoothing the linear quantile regression estimator, and develop two bootstrap methods, a novel pivotal bootstrap and the nonparametric bootstrap, for our conditional mode estimator. Building on high-dimensional Gaussian approximation techniques, we establish the validity of simultaneous confidence rectangles constructed from the two bootstrap met…
We propose new resampling-based approaches to construct asymptotically valid time simultaneous confidence bands for cumulative hazard functions in multi-state Cox models. In particular, we exemplify the methodology in detail for the simple Cox model with time dependent covariates, where the data may be subject to independent right-censoring or left-truncation. In extensive simulations we investigate their finite sample behaviour. Finally, the methods are utilized to analyze an empirical example.
In this paper we propose an autoregressive wild bootstrap method to construct confidence bands around a smooth deterministic trend. The bootstrap method is easy to implement and does not require any adjustments in the presence of missing data, which makes it particularly suitable for climatological applications. We establish the asymptotic validity of the bootstrap method for both pointwise and simultaneous confidence bands under general conditions, allowing for general patterns of missing data, serial dependence and heteroskedasticity. The finite sample properties of the method are studied in…
This paper investigates the theoretical underpinnings of two fundamental statistical inference problems, the construction of confidence sets and large-scale simultaneous hypothesis testing, in the presence of heavy-tailed data. With heavy-tailed observation noise, finite sample properties of the least squares-based methods, typified by the sample mean, are suboptimal both theoretically and empirically. In this paper, we demonstrate that the adaptive Huber regression, integrated with the multiplier bootstrap procedure, provides a useful robust alternative to the method of least squares. Our the…
Gaussian and Bootstrap Approximations for Suprema of Empirical Processes
本文提出经验过程上确界分布的非渐近高斯逼近与基于截断Karhunen-Loève分解的Bootstrap方法，适用于非Donsker类且条件更简单，并成功应用于高维统计中的三个基本推断问题。
The authors (Cason, Friedman and Hopkins, Reviews of Economics Studies, 2014) claimed a result that the treatments (using simultaneous matching in discrete time) replicate previous results that exhibit weak or no cycles. After correct two mathematical mistakes in their cycles tripwire algorithm, we research the cycles by scanning the tripwire in the full strategy space of the games and we find significant cycles missed by the authors. So we suggest that, all of the treatments (using simultaneous matching in discrete time) exhibit significant cycles.
The Bonferroni adjustment, or the union bound, is commonly used to study rate optimality properties of statistical methods in high-dimensional problems. However, in practice, the Bonferroni adjustment is overly conservative. The extreme value theory has been proven to provide more accurate multiplicity adjustments in a number of settings, but only on ad hoc basis. Recently, Gaussian approximation has been used to justify bootstrap adjustments in large scale simultaneous inference in some general settings when $n \gg (\log p)^7$, where $p$ is the multiplicity of the inference problem and $n$ is…
Simultaneous Inference in Multiple Matrix-Variate Graphs for High-Dimensional Neural Recordings
本文提出了一种统一框架，结合组惩罚回归和高维高斯近似自助法，用于高维神经记录中多个矩阵变量图的同时推断，实现对任意大小边子集的全局检验。
Self-convolved Bootstrap for M-regression under Complex Temporal Dynamics
针对协变量与误差可交叉依赖的非平稳时变系数 M 回归，提出单参数自卷积 bootstrap，实现 √n 一致推断及多类统一检验，并应用于气候与股票数据。
Bootstrap inference for linear regression between variables that are never jointly observed: application in in vivo experiments
针对无法同时观测的变量间线性回归系数估计问题，提出基于矩和最优传输理论的估计量，并开发分层自助法构建置信区间，在小鼠体内实验中成功识别出朴素方法无法发现的生物标志物关系。
Simultaneous Inference for Time Series Functional Linear Regression
本文提出一种统一的乘数Bootstrap方法，用于构建时间序列标量-函数线性回归系数函数的联合置信带，该方法在粗糙度惩罚估计下具有正确的覆盖概率渐近性，并对不一致估计的标准差具有渐近鲁棒性。
Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered, hierarchical or longitudinal data are investigated. Nonetheless, statistical tools for valid simultaneous inference for mixed parameters are rare. This is surprising because one often faces inferential problems beyond the pointwise examination of fixed or mixed parameters. For example, there is an interest in a comparative analysis of cluster-level parameters or subject-specific estimates in studies with repeated measurements. We discuss…
We study the residual bootstrap (RB) method in the context of high-dimensional linear regression. Specifically, we analyze the distributional approximation of linear contrasts $c^{\top} (\hatβ_ρ-β)$, where $\hatβ_ρ$ is a ridge-regression estimator. When regression coefficients are estimated via least squares, classical results show that RB consistently approximates the laws of contrasts, provided that $p\ll n$, where the design matrix is of size $n\times p$. Up to now, relatively little work has considered how additional structure in the linear model may extend the validity of RB to the settin…
The V-fold jackknife for semiparametric inference: variance estimation, confidence intervals, and simultaneous confidence bands
研究针对半参数推断开发V折刀切法，它计算高效且理论合理，仅需V次留一法重拟合，利用伪值经验离散度量化不确定性，给出有效置信区间和同时置信带，扩展理论到特定估计量，模拟证实其可靠推断。
This paper studies the Gaussian approximation of high-dimensional and non-degenerate U-statistics of order two under the supremum norm. We propose a two-step Gaussian approximation procedure that does not impose structural assumptions on the data distribution. Specifically, subject to mild moment conditions on the kernel, we establish the explicit rate of convergence that decays polynomially in sample size for a high-dimensional scaling limit, where the dimension can be much larger than the sample size. We also supplement a practical Gaussian wild bootstrap method to approximate the quantiles …
Simultaneous Inference for Non-Stationary Random Fields, with Application to Gridded Data Analysis
本文针对一般非平稳非高斯随机场，提出基于位移随机场非线性建模的同时非参数推断框架，并开发局部加权乘子自助算法，实现高维稀疏线性形式的统一统计推断。
In this paper, we consider the time-inhomogeneous nonlinear time series regression for a general class of locally stationary time series. On one hand, we propose sieve nonparametric estimators for the time-varying regression functions which can achieve the min-max optimal rate. On the other hand, we develop a unified simultaneous inferential theory which can be used to conduct both structural and exact form testings on the functions. Our proposed statistics are powerful even under locally weak alternatives. We also propose a multiplier bootstrapping procedure for practical implementation. Our …
Simultaneous Inference for Covariance and Precision Matrices of Long-Range Dependent Time Series
本文提出一种Berry-Esseen型正态近似结果，用于长期依赖时间序列协方差和精度矩阵的有限样本界推断，采用鞅和m依赖近似及三元块构造方法，支持高维设置和自助法验证。
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