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模型选择后具有一致有效性的置信区间AI 解读

We suggest general methods to construct asymptotically uniformly valid confidence intervals post-model-selection. The constructions are based on principles recently proposed by Berk et al. (Ann. Statist. 41 (2013) 802–837). In particular, the candidate models used can be misspecified, the target of inference is model-specific, and coverage is guaranteed for any data-driven model selection procedure. After developing a general theory, we apply our methods to practically…

通过样本分割一致选择变点数量AI 解读

In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and…

This paper proposes a numerical bootstrap method that is consistent in many cases where the standard bootstrap is known to fail and where the $m$-out-of-$n$ bootstrap and subsampling have been the most commonly used inference approaches. We provide asymptotic analysis under both fixed and drifting parameter sequences, and we compare the approximation error of the numerical bootstrap with that of the $m$-out-of-$n$ bootstrap and subsampling. Finally, we discuss applications…

典范与弯曲指数族随机图模型的集中性和一致性结果AI 解读

Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple example of a random graph with additional structure is a random graph with neighborhoods and local dependence within neighborhoods. We develop the first concentration and consistency results for maximum likelihood and $M$-estimators of a wide…

多臂老虎机问题：一种有效率的非参数解法AI 解读

Lai and Robbins (Adv. in Appl. Math. 6 (1985) 4–22) and Lai (Ann. Statist. 15 (1987) 1091–1114) provided efficient parametric solutions to the multi-armed bandit problem, showing that arm allocation via upper confidence bounds (UCB) achieves minimum regret. These bounds are constructed from the Kullback–Leibler information of the reward distributions, estimated from specified parametric families. In recent years, there has been renewed interest in the multi-armed bandit…

弱可识别性下的主成分方向检验AI 解读

We consider the problem of testing, on the basis of a $p$-variate Gaussian random sample, the null hypothesis $\mathcal{H}_{0}:\boldsymbol{\theta}_{1}=\boldsymbol{\theta}_{1}^{0}$ against the alternative $\mathcal{H}_{1}:\boldsymbol{\theta}_{1}\neq \boldsymbol{\theta}_{1}^{0}$, where $\boldsymbol{\theta}_{1}$ is the “first” eigenvector of the underlying covariance matrix and $\boldsymbol{\theta}_{1}^{0}$ is a fixed unit $p$-vector. In the classical setup where eigenvalues $\lambda_{1}>\lambda_{2}\geq \cdots \geq \lambda_{p}$…

稀疏高维回归：可扩展精确算法与相变AI 解读

We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse regression problem for sample sizes $n$ and number of regressors $p$ in the 100,000s, that is, two orders of magnitude better than the current state of the art, in seconds. The ability to solve the problem for very high dimensions allows us to…

非标准条件下基于 M 估计量的 Bootstrap 置信域AI 解读

Suppose that a confidence region is desired for a subvector $\theta $ of a multidimensional parameter $\xi =(\theta ,\psi )$, based on an M-estimator $\hat{\xi }_{n}=(\hat{\theta }_{n},\hat{\psi }_{n})$ calculated from a random sample of size $n$. Under nonstandard conditions $\hat{\xi }_{n}$ often converges at a nonregular rate $r_{n}$, in which case consistent estimation of the distribution of $r_{n}(\hat{\theta }_{n}-\theta )$, a pivot commonly chosen for confidence…

随机梯度下降中模型参数的统计推断AI 解读

The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing works focus on the convergence of the objective function or the error of the obtained solution, we investigate the problem of statistical inference of true model parameters based on SGD when the population loss function is strongly convex and satisfies certain smoothness conditions. Our main…

多层网络一致社区检测的谱方法与矩阵分解方法AI 解读

We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network using methods based on the spectral clustering or a low-rank matrix factorization. As a general theme, these “intermediate fusion” methods involve obtaining a low column rank matrix by optimizing an objective function and then using the columns of the matrix for clustering. However, the theoretical properties of these methods remain…

一元全变差去噪与趋势滤波的自适应风险界AI 解读

We study trend filtering, a relatively recent method for univariate nonparametric regression. For a given integer $r\geq1$, the $r$th order trend filtering estimator is defined as the minimizer of the sum of squared errors when we constrain (or penalize) the sum of the absolute $r$th order discrete derivatives of the fitted function at the design points. For $r=1$, the estimator reduces to total variation regularization which has received much attention in the statistics and…

加权随机区块模型中社群估计的最优速率AI 解读

Community identification in a network is an important problem in fields such as social science, neuroscience and genetics. Over the past decade, stochastic block models (SBMs) have emerged as a popular statistical framework for this problem. However, SBMs have an important limitation in that they are suited only for networks with unweighted edges; in various scientific applications, disregarding the edge weights may result in a loss of valuable information. We study a…

基于包络模型的稀疏偏最小二乘AI 解读

Sparse partial least squares (SPLS) is widely used in applied sciences as a method that performs dimension reduction and variable selection simultaneously in linear regression. Several implementations of SPLS have been derived, among which the SPLS proposed in Chun and Keleş (J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 3–25) is very popular and highly cited. However, for all of these implementations, the theoretical properties of SPLS are largely unknown. In this…

In sequential causal inference, two types of causal effects are of practical interest, namely, the causal effect of the treatment regime (called the sequential causal effect) and the blip effect of treatment on the potential outcome after the last treatment. The well-known $G$-formula expresses these causal effects in terms of the standard parameters. In this article, we obtain a new $G$-formula that expresses these causal effects in terms of the point observable effects of…

模型辅助变量聚类：极小极大最优恢复与算法AI 解读

The problem of variable clustering is that of estimating groups of similar components of a $p$-dimensional vector $X=(X_{1},\ldots ,X_{p})$ from $n$ independent copies of $X$. There exists a large number of algorithms that return data-dependent groups of variables, but their interpretation is limited to the algorithm that produced them. An alternative is model-based clustering, in which one begins by defining population level clusters relative to a model that embeds notions…

稀疏切片逆回归：最优收敛率与自适应估计AI 解读

Sliced inverse regression (SIR) is an innovative and effective method for sufficient dimension reduction and data visualization. Recently, an impressive range of penalized SIR methods has been proposed to estimate the central subspace in a sparse fashion. Nonetheless, few of them considered the sparse sufficient dimension reduction from a decision-theoretic point of view. To address this issue, we in this paper establish the minimax rates of convergence for estimating the…

高维逻辑回归中最大似然估计存在性的相变AI 解读

This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp “phase transition.” We introduce an explicit boundary curve $h_{\mathrm{MLE}}$, parameterized by two scalars measuring the overall magnitude of the unknown sequence of regression coefficients, with the following property: in the limit of large sample sizes $n$ and number of features $p$ proporti…

两步半参数经验似然推断AI 解读

In both parametric and certain nonparametric statistical models, the empirical likelihood ratio satisfies a nonparametric version of Wilks’ theorem. For many semiparametric models, however, the commonly used two-step (plug-in) empirical likelihood ratio is not asymptotically distribution-free, that is, its asymptotic distribution contains unknown quantities, and hence Wilks’ theorem breaks down. This article suggests a general approach to restore Wilks’ phenomenon in…

无标签网络的平均：几何刻画与渐近行为AI 解读

It is becoming increasingly common to see large collections of network data objects, that is, data sets in which a network is viewed as a fundamental unit of observation. As a result, there is a pressing need to develop network-based analogues of even many of the most basic tools already standard for scalar and vector data. In this paper, our focus is on averages of unlabeled, undirected networks with edge weights. Specifically, we (i) characterize a certain notion of the…

通过阈值化 Tyler M 估计量进行稳健稀疏协方差估计AI 解读

Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental task in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Toward bridging this gap, in this work we consider estimating a sparse shape matrix from $n$ samples following a possibly heavy-tailed elliptical distribution. We propose estimators based on thresholding either Tyler’s M-estimator or its regularized variant. We…

二水平多因子实验中的重随机化AI 解读

With many pretreatment covariates and treatment factors, the classical factorial experiment often fails to balance covariates across multiple factorial effects simultaneously. Therefore, it is intuitive to restrict the randomization of the treatment factors to satisfy certain covariate balance criteria, possibly conforming to the tiers of factorial effects and covariates based on their relative importances. This is rerandomization in factorial experiments. We study the…

低效率区域模式建模：贝叶斯地理加性面板随机前沿方法AI 解读

We propose a flexible Bayesian approach to inefficiency modelling that accounts for regional patterns of local performance. The model allows for a separated treatment of individual heterogeneity and determinants of inefficiency. Regional dependence structures and location-specific unobserved spatial heterogeneity are modelled via geoadditive predictors in the inefficiency term of the stochastic frontier model. Inference becomes feasible through Markov chain Monte Carlo…

多工具变量下的稳健估计AI 解读

Linear instrumental variables models are widely used in empirical work, but often associated with low estimator precision. This paper proposes an estimator that is robust to outliers and shows that the estimator is minimax optimal in a class of estimators that includes the limited maximum likelihood estimator (LIML). Intuitively, this optimal robust estimator combines LIML with Winsorization of the structural residuals and the Winsorization leads to improved precision under…

基于高频数据的高维最小方差组合估计AI 解读

This paper studies the estimation of high-dimensional minimum variance portfolio (MVP) based on the high frequency returns which can exhibit heteroscedasticity and possibly be contaminated by microstructure noise. Under certain sparsity assumptions on the precision matrix, we propose estimators of the MVP and prove that our portfolios asymptotically achieve the minimum variance in a sharp sense. In addition, we introduce consistent estimators of the minimum variance, which…