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具有块结构的大规模统计推断AI 解读

The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale multiple testing that is inherent in these problems. Here, we show that fundamentally more powerful statistical inference is possible when there is some structure in the signal that can be exploited, for example, if the signal is clustered in…

Wasserstein 距离下光滑密度的极小极大估计AI 解读

We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates for this problem for general Wasserstein distances for two classes of densities: smooth probability densities on [0,1]d bounded away from 0, and sub-Gaussian densities lying in the Hölder class Cs, s∈(0,1). Unlike classical nonparametric…

多元最大稳定分布贝叶斯推断的一致性AI 解读

Predicting extreme events is important in many applications in risk analysis. Extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction. Although various Bayesian inferential procedures have been proposed in the literature of univariate extremes and some for multivariate extremes, the study of their asymptotic properties has been left largely untouched. In this paper we focus on…

用高阶批判检验比较大型频数表中的稀疏微弱差异AI 解读

We adapt Higher Criticism (HC) to the comparison of two frequency tables which may—or may not—exhibit moderate differences between the tables in some unknown, relatively small subset out of a large number of categories. Our analysis of the power of the proposed HC test quantifies the rarity and size of assumed differences and applies moderate deviations-analysis to determine the asymptotic powerfulness/powerlessness of our proposed HC procedure. Our analysis considers the…

密度水平集经验估计量的立方根弱收敛AI 解读

Given n independent random vectors with common density f on Rd, we study the weak convergence of three empirical-measure based estimators of the convex λ-level set Lλ of f, namely the excess mass set, the minimum volume set and the maximum probability set, all selected from a class of convex sets A that contains Lλ. Since these set-valued estimators approach Lλ, even the formulation of their weak convergence is nonstandard. We identify the joint limiting distribution of the…

重新审视岭回归：去偏、阈值化与自助法AI 解读

The success of the Lasso in the era of high-dimensional data can be attributed to its conducting an implicit model selection, that is, zeroing out regression coefficients that are not significant. By contrast, classical ridge regression cannot reveal a potential sparsity of parameters, and may also introduce a large bias under the high-dimensional setting. Nevertheless, recent work on the Lasso involves debiasing and thresholding, the latter in order to further enhance the…

部分线性Cox模型的深度学习方法AI 解读

While deep learning approaches to survival data have demonstrated empirical success in applications, most of these methods are difficult to interpret and mathematical understanding of them is lacking. This paper studies the partially linear Cox model, where the nonlinear component of the model is implemented using a deep neural network. The proposed approach is flexible and able to circumvent the curse of dimensionality, yet it facilitates interpretability of the effects of…

ARFIMA 过程的一致阶数选择AI 解读

Estimating the orders of the autoregressive fractionally integrated moving average (ARFIMA) model has been a long-standing problem in time series analysis. This paper tackles this challenge by establishing the consistency of the Bayesian information criterion (BIC) for ARFIMA models with independent errors. Since the memory parameter of the model can be any real number, this consistency result is valid for short memory, long memory and nonstationary time series. This paper…

利用多个可能无效的工具变量构造证据因子AI 解读

Valid instrumental variables enable treatment effect inference even when selection into treatment is biased by unobserved confounders. When multiple candidate instruments are available, but some of them are possibly invalid, the previously proposed reinforced design enables one or more nearly independent valid analyses that depend on very different assumptions. That is, we can perform evidence factor analysis. However, the validity of the reinforced design depends crucially…

多因素实验中的设计可容许性与 de la Garza 现象AI 解读

The determination of an optimal design for a given regression problem is an intricate optimization problem, especially for models with multivariate predictors. Design admissibility and invariance are main tools to reduce the complexity of the optimization problem and have been successfully applied for models with univariate predictors. In particular, several authors have developed sufficient conditions for the existence of minimally supported designs in univariate models,…

低次多项式估计的计算障碍AI 解读

One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for such problems: it has been demonstrated in various settings that low-degree polynomials of the data can match the statistical performance of the best known polynomial-time algorithms. Prior work has studied the power of low-degree…

奇异信息与参数边界附近的置信域及其混合模型应用AI 解读

We propose confidence regions with asymptotically correct uniform coverage probability of parameters whose Fisher information matrix can be singular at important points of the parameter set. Our work is motivated by the need for reliable inference on scale parameters close or equal to zero in mixed models, which is obtained as a special case. The confidence regions are constructed by inverting a continuous extension of the score test statistic standardized by expected…

前 k 名排序的部分恢复：极大似然最优性与谱方法的次优性AI 解读

Given partially observed pairwise comparison data generated by the Bradley–Terry–Luce (BTL) model, we study the problem of top-k ranking. That is, to optimally identify the set of top-k players. We derive the minimax rate with respect to a normalized Hamming loss. This provides the first result in the literature that characterizes the partial recovery error in terms of the proportion of mistakes for top-k ranking. We also derive the optimal signal to noise ratio condition…

局部弗雷歇回归的一致收敛及其在极值定位与时间配准中的应用AI 解读

Local Fréchet regression is a nonparametric regression method for metric space valued responses and Euclidean predictors, which can be utilized to obtain estimates of smooth trajectories taking values in general metric spaces from noisy metric space valued random objects. We derive uniform rates of convergence, which so far have eluded theoretical analysis of this method, for both fixed and random target trajectories, where we utilize tools from empirical processes. These…

Variance estimation is important for statistical inference. It becomes nontrivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or sub-optimally handle these nuisance structures. This paper develops a general framework for the estimation of the long-run variance for time series with nonconstant means. The building blocks are difference statistics. The proposed class of estimators is general…

双重去偏 lasso：隐藏混杂下的高维推断AI 解读

Inferring causal relationships or related associations from observational data can be invalidated by the existence of hidden confounding. We focus on a high-dimensional linear regression setting, where the measured covariates are affected by hidden confounding and propose the doubly debiased lasso estimator for individual components of the regression coefficient vector. Our advocated method simultaneously corrects both the bias due to estimation of high-dimensional…

低秩张量推断：无需去偏AI 解读

In this paper, we consider the statistical inference for several low-rank tensor models. Specifically, in the Tucker low-rank tensor PCA or regression model, provided with any estimates achieving some attainable error rate, we develop the data-driven confidence regions for the singular subspace of the parameter tensor based on the asymptotic distribution of an updated estimate by two-iteration alternating minimization. The asymptotic distributions are established under some…

裂区实验中设计式与模型式因果推断的协调AI 解读

The split-plot design arose from agricultural science with experimental units, also known as the subplots, nested within groups known as the whole plots. It assigns different interventions at the whole-plot and subplot levels, respectively, providing a convenient way to accommodate hard-to-change factors. By design, subplots within the same whole plot receive the same level of the whole-plot intervention, and thereby induce a group structure on the final treatment…

尖峰协方差矩阵主成分的统计推断AI 解读

In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high-dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. In particular, we derive the joint distribution of the extreme eigenvalues and the generalized components of the associated eigenvectors, that is, the projections of the eigenvectors onto arbitrary given direction, assuming that the dimension and sample…

未知零假设分布下的错误发现率控制：能否模拟理想程序？AI 解读

Classical multiple testing theory prescribes the null distribution, which is often too stringent an assumption for nowadays large scale experiments. This paper presents theoretical foundations to understand the limitations caused by ignoring the null distribution, and how it can be properly learned from the same data set, when possible. We explore this issue in the setting where the null distributions are Gaussian with unknown rescaling parameters (mean and variance) whereas…

离散结构恢复的迭代算法AI 解读

We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, signs of regression coefficients, cyclic shifts and even group elements from a unified perspective. A simple iterative algorithm is proposed for discrete structure recovery, which generalizes methods including Lloyd’s algorithm and the power…

紧致度量空间随机场渐近最优线性预测的充要条件AI 解读

Optimal linear prediction (aka. kriging) of a random field {Z(x)}x∈X indexed by a compact metric space (X,dX) can be obtained if the mean value function m:X→R and the covariance function ϱ:X×X→R of Z are known. We consider the problem of predicting the value of Z(x∗) at some location x∗∈X based on observations at locations {xj}j=1n, which accumulate at x∗ as n→∞ (or, more generally, predicting φ(Z) based on {φj(Z)}j=1n for linear functionals φ,φ1,…,φn). Our main result…

多重插补数据集的一般且可实施检验AI 解读

Multiple imputation (MI) is a technique especially designed for handling missing data in public-use datasets. It allows analysts to perform incomplete-data inference straightforwardly by using several already imputed datasets released by the dataset owners. However, the existing MI tests require either a restrictive assumption on the missing-data mechanism, known as equal odds of missing information (EOMI), or an infinite number of imputations. Some of them also require…

基于平均 Fréchet 导数的函数型充分降维AI 解读

Sufficient dimension reduction (SDR) embodies a family of methods that aim for reduction of dimensionality without loss of information in a regression setting. In this article, we propose a new method for nonparametric function-on-function SDR, where both the response and the predictor are a function. We first develop the notions of functional central mean subspace and functional central subspace, which form the population targets of our functional SDR. We then introduce an…