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条件平均处理效应函数的双重稳健一致置信带AI 解读

Summary In this paper, we propose a doubly robust method to estimate the heterogeneity of the average treatment effect with respect to observed covariates of interest. We consider a situation where a large number of covariates are needed for identifying the average treatment effect but the covariates of interest for analyzing heterogeneity are of much lower dimension. Our proposed estimator is doubly robust and avoids the curse of dimensionality. We propose a uniform…

多重假设检验中的混杂因素调整AI 解读

We consider large-scale studies in which thousands of significance tests are performed simultaneously. In some of these studies, the multiple testing procedure can be severely biased by latent confounding factors such as batch effects and unmeasured covariates that correlate with both primary variable(s) of interest (e.g., treatment variable, phenotype) and the outcome. Over the past decade, many statistical methods have been proposed to adjust for the confounders in…

高维时间序列的高斯近似AI 解读

We consider the problem of approximating sums of high dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size $n$, the dimension $p$, the moment condition and the dependence of the underlying processes. We also consider an estimator for long-run covariance matrices and study its convergence properties. Our results allow constructing simultaneous…

可扩展因子分析AI 解读

Bayesian sparse factor models have proven useful for characterizing dependence in multivariate data, but scaling computation to large numbers of samples and dimensions is problematic. We propose expandable factor analysis for scalable inference in factor models when the number of factors is unknown. The method relies on a continuous shrinkage prior for efficient maximum a posteriori estimation of a low-rank and sparse loadings matrix. The structure of the prior leads to an…

复杂生存数据的 non-strange weird 重抽样AI 解读

This paper introduces a new data-dependent multiplier bootstrap for nonparametric analysis of survival data, possibly subject to competing risks. The nw procedure includes the general wild bootstrap and the weird bootstrap as special cases. The data may be subject to independent right-censoring and left-truncation. The asymptotic correctness of the proposed resampling procedure is proven under standard assumptions. Simulation results on time-simultaneous inference suggest…

p-filter：分组假设的多层错误发现率控制AI 解读

Summary In many practical applications of multiple testing, there are natural ways to partition the hypotheses into groups by using the structural, spatial or temporal relatedness of the hypotheses, and this prior knowledge is not used in the classical Benjamini–Hochberg procedure for controlling the false discovery rate (FDR). When one can define (possibly several) such partitions, it may be desirable to control the group FDR simultaneously for all partitions (as special…

未知依赖结构下的错误发现比例估计AI 解读

Summary Large-scale multiple testing with correlated test statistics arises frequently in much scientific research. Incorporating correlation information in approximating the false discovery proportion (FDP) has attracted increasing attention in recent years. When the covariance matrix of test statistics is known, Fan and his colleagues provided an accurate approximation of the FDP under arbitrary dependence structure and some sparsity assumption. However, the covariance…

高维尖峰协方差经验特征结构的渐近理论AI 解读

We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size, and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size, and dimensionality play in principal component analysis. Our results are a natural extension of those…

高维线性模型的同时推断AI 解读

This article proposes a bootstrap-assisted procedure to conduct simultaneous inference for high-dimensional sparse linear models based on the recent desparsifying Lasso estimator. Our procedure allows the dimension of the parameter vector of interest to be exponentially larger than sample size, and it automatically accounts for the dependence within the desparsifying Lasso estimator. Moreover, our simultaneous testing method can be naturally coupled with the margin screening…

依赖条件下恢复高维均值稀疏差异的速率最优方法AI 解读

The paper considers the problem of recovering the sparse different components between two high-dimensional means of column-wise dependent random vectors. We show that dependence can be utilized to lower the identification boundary for signal recovery. Moreover, an optimal convergence rate for the marginal false nondiscovery rate (mFNR) is established under dependence. The convergence rate is faster than the optimal rate without dependence. To recover the sparse signal…

A topological multiple testing scheme is presented for detecting peaks in images under stationary ergodic Gaussian noise, where tests are performed at local maxima of the smoothed observed signals. The procedure generalizes the one-dimensional scheme of [31] to Euclidean domains of arbitrary dimension. Two methods are developed according to two different ways of computing p-values: (i) using the exact distribution of the height of local maxima, available explicitly when the…

识别两样本差异的概率多分辨率扫描AI 解读

Summary We propose a multi-resolution scanning approach to identifying two-sample differences. Windows of multiple scales are constructed through nested dyadic partitioning on the sample space and a hypothesis regarding the two-sample difference is defined on each window. Instead of testing the hypotheses on different windows independently, we adopt a joint graphical model, namely a Markov tree, on the null or alternative states of these hypotheses to incorporate spatial…

时变系数分位数回归的非参数推断AI 解读

The article considers nonparametric inference for quantile regression models with time-varying coefficients. The errors and covariates of the regression are assumed to belong to a general class of locally stationary processes and are allowed to be cross-dependent. Simultaneous confidence tubes (SCTs) and integrated squared difference tests (ISDTs) are proposed for simultaneous nonparametric inference of the latter models with asymptotically correct coverage probabilities and…

稀疏信号的最优筛选与发现：多阶段高通量研究应用AI 解读

Summary A common feature in large-scale scientific studies is that signals are sparse and it is desirable to narrow down significantly the focus to a much smaller subset in a sequential manner. We consider two related data screening problems: one is to find the smallest subset such that it virtually contains all signals and another is to find the largest subset such that it essentially contains only signals. These screening problems are closely connected to but distinct from…

多重检验的族级分离率AI 解读

Starting from a parallel between some minimax adaptive tests of a single null hypothesis, based on aggregation approaches, and some tests of multiple hypotheses, we propose a new second kind error-related evaluation criterion, as the core of an emergent minimax theory for multiple tests. Aggregation-based tests, proposed for instance by Baraud [Bernoulli 8 (2002) 577–606], Baraud, Huet and Laurent [Ann. Statist. 31 (2003) 225–251] or Fromont and Laurent [Ann. Statist. 34…

准稀疏计数数据的贝叶斯推断AI 解读

There is growing interest in analysing high-dimensional count data, which often exhibit quasi-sparsity corresponding to an overabundance of zeros and small nonzero counts. Existing methods for analysing multivariate count data via Poisson or negative binomial log-linear hierarchical models with zero-inflation cannot flexibly adapt to quasi-sparse settings. We develop a new class of continuous local-global shrinkage priors tailored to quasi-sparse counts. Theoretical…

条件风险价值：半参数估计与推断AI 解读

Conditional Value-at-Risk (CVaR) plays an important role in financial risk management. Nonparametric CVaR estimation suffers from the “curse of dimensionality” and slow convergence rate. To overcome these issues, we study semiparametric CVaR estimation and inference for parametric model with nonparametric noise distribution. Under a general framework that allows for many widely used time series models, we propose a semiparametric CVaR estimator that achieves the parametric…

高维相关随机效应面板模型中的预言不等式、变量选择与一致有效推断AI 解读

In this paper we study high-dimensional correlated random effects panel data models. Our setting is useful as it allows including time invariant covariates as under random effects yet allows for correlation between covariates and unobserved heterogeneity as under fixed effects. We use the Mundlak–Chamberlain device to model this correlation. Allowing for a flexible correlation structure naturally leads to a high-dimensional model in which least squares estimation easily…

高维线性模型中单个回归系数的检验AI 解读

In linear regression models with high dimensional data, the classical z-test (or t-test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the…

函数型数据的极端深度及其应用AI 解读

We propose a new notion called “extremal depth” (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme “outlyingness.” ED has several desirable properties that are not shared by other notions and is especially well suited for obtaining central regions of functional data and function spaces. In particular: (a) the central region achieves the nominal (desired) simultaneous…

短程与长程依赖下单调函数的推断：置信区间与新的普适极限AI 解读

We introduce new point-wise confidence interval estimates for monotone functions observed with additive, dependent noise. Our methodology applies to both short- and long-range dependence regimes for the errors. The interval estimates are obtained via the method of inversion of certain discrepancy statistics. This approach avoids the estimation of nuisance parameters such as the derivative of the unknown function, which previous methods are forced to deal with. The resulting…

学生化两样本 U 统计量的 Cramér 型中等偏差及应用AI 解读

Two-sample $U$-statistics are widely used in a broad range of applications, including those in the fields of biostatistics and econometrics. In this paper, we establish sharp Cramér-type moderate deviation theorems for Studentized two-sample $U$-statistics in a general framework, including the two-sample $t$-statistic and Studentized Mann–Whitney test statistic as prototypical examples. In particular, a refined moderate deviation theorem with second-order accuracy is…

双成分混合模型的估计及其多重检验应用AI 解读

Summary We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution non-parametrically, given independent and identically distributed data from the mixture model, using ideas from shape-restricted function estimation. We establish the consistency of our estimators. We find the rate of convergence and asymptotic limit of the estimator for the mixing proportion. Completely automated…

依赖情形下自归一化的 Cramér 型中等偏差AI 解读

We establish a Cramér-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than the non-self-normalized counterpart. The range of the moderate deviation is shown to depend on the moment condition and the degree of dependence of the underlying processes. We consider three types of self-normalization: the equal-block scheme, the big-block-small-block scheme and the interlacing scheme.…