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通过多元谱的总Frobenius范数进行模型识别AI 解读

Abstract We study the integral of the Frobenius norm as a measure of the discrepancy between two multivariate spectra. Such a measure can be used to fit time series models, and ensures proximity between model and process at all frequencies of the spectral density—this is more demanding than Kullback–Leibler discrepancy, which is instead related to one-step ahead forecasting performance. We develop new asymptotic results for linear and quadratic functionals of the…

异方差或无处理基准效应模型误设下最优个体化处理规则的高效学习AI 解读

Abstract Recent development in data-driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, researchers can search for the optimal individualized treatment rule (ITR) that maximizes the expected outcome. Existing methods typically require initial estimation of some nuisance models. The double robustness property that can protect from misspecification of either the…

利用Lasso进行效应修饰的选择后推断AI 解读

Abstract Effect modification occurs when the effect of the treatment on an outcome varies according to the level of other covariates and often has important implications in decision-making. When there are tens or hundreds of covariates, it becomes necessary to use the observed data to select a simpler model for effect modification and then make valid statistical inference. We propose a two-stage procedure to solve this problem. First, we use Robinson's transformation to…

交错实施下的合成控制法AI 解读

Abstract Staggered adoption of policies by different units at different times creates promising opportunities for observational causal inference. Estimation remains challenging, however, and common regression methods can give misleading results. A promising alternative is the synthetic control method (SCM), which finds a weighted average of control units that closely balances the treated unit’s pre-treatment outcomes. In this paper, we generalize SCM, originally designed to…

有限总体因果推断中的高斯预枢轴化AI 解读

Abstract In finite population causal inference exact randomization tests can be constructed for sharp null hypotheses, hypotheses which impute the missing potential outcomes. Oftentimes inference is instead desired for the weak null that the sample average of the treatment effects takes on a particular value while leaving the subject-specific treatment effects unspecified. Tests valid for sharp null hypotheses can be anti-conservative should only the weak null hold. We…

针对两个响应变量交互关系的有效降维AI 解读

Abstract In this paper, we propose the novel theory and methodologies for dimension reduction with respect to the interaction between two response variables, which is a new research problem that has wide applications in missing data analysis, causal inference, graphical models, etc. We formulate the parameters of interest to be the locally and the globally efficient dimension reduction subspaces, and justify the generality of the corresponding low-dimensional assumption. We…

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…

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 HSIC 的自适应独立性检验AI 解读

The Hilbert–Schmidt Independence Criterion (HSIC) is a dependence measure based on reproducing kernel Hilbert spaces that is widely used to test independence between two random vectors. Remains the delicate choice of the kernel. In this work, we develop a new HSIC-based aggregated procedure which avoids such a kernel choice, and provide theoretical guarantees for this procedure. To achieve this, on the one hand, we introduce non-asymptotic single tests based on Gaussian…

利用辅助信息的大规模多重检验最优错误发现率控制AI 解读

Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are available. Exploiting such auxiliary information can boost statistical power. To this end, we propose a framework based on a two-group mixture model with varying probabilities of being null for different hypotheses a priori, where a…

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…

非稀疏高维线性模型的可检验性AI 解读

Understanding statistical inference under possibly nonsparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity of the corresponding row of the precision matrix of the covariates, not the sparsity of the regression coefficients. We develop new concepts of uniform and essentially uniform nontestability that allow the study of limitations of tests…

兼具多种性质的高斯均值稳健估计量AI 解读

The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time, which is at most polynomial in dimension, sample size and the logarithm of the inverse of the contamination rate. Second, it is equivariant by translations, uniform scaling and orthogonal transformations. Third, it has a high breakdown…

高维面板数据截面独立性的最大值—求和检验AI 解读

We consider a testing problem for cross-sectional independence for high-dimensional panel data, where the number of cross-sectional units is potentially much larger than the number of observations. The cross-sectional independence is described through linear regression models. We study three tests named the sum, the max and the max-sum tests, where the latter two are new. The sum test is initially proposed by Breusch and Pagan (1980). We design the max and sum tests for…

最优传输定义的多元秩与分位数：一致性、速率和非参数检验AI 解读

In this paper, we study multivariate ranks and quantiles, defined using the theory of optimal transport, and build on the work of Chernozhukov et al. (Ann. Statist. 45 (2017) 223–256) and Hallin et al. (Ann. Statist. 49 (2021) 1139–1165). We study the characterization, computation and properties of the multivariate rank and quantile functions and their empirical counterparts. We derive the uniform consistency of these empirical estimates to their population versions, under…

通过子图抽样估计网络模体：四阶矩现象AI 解读

Network sampling is an indispensable tool for understanding features of large complex networks where it is practically impossible to search over the entire graph. In this paper, we develop a framework for statistical inference for counting network motifs, such as edges, triangles and wedges, in the widely used subgraph sampling model, where each vertex is sampled independently, and the subgraph induced by the sampled vertices is observed. We derive necessary and sufficient…

网络矩统计量的 Edgeworth 展开AI 解读

Network method of moments (Ann. Statist. 39 (2011) 2280–2301) is an important tool for nonparametric network inference. However, there has been little investigation on accurate descriptions of the sampling distributions of network moment statistics. In this paper, we present the first higher-order accurate approximation to the sampling CDF of a studentized network moment by Edgeworth expansion. In sharp contrast to classical literature on noiseless U-statistics, we show that…

多变量时间序列的平稳藤 Copula 模型AI 解读

Multivariate time series exhibit two types of dependence: across variables and across time points. Vine copulas are graphical models for the dependence and can conveniently capture both types of dependence in the same model. We derive the maximal class of graph structures that guarantee stationarity under a natural and verifiable condition called translation invariance. We propose computationally efficient methods for estimation, simulation, prediction, and uncertainty…

评《具有随机波动率和非共轭先验的大型贝叶斯向量自回归》AI 解读

Fully Bayesian inference in a vector autoregression with stochastic volatility (VAR-SV) typically relies on simulations from a multi-step Markov chain Monte Carlo (MCMC) algorithm. Carriero et al. (2019) propose a new, faster, “triangular” algorithm (TA) to replace the systemwide algorithm (SWA) in the most time-consuming step of the VAR-SV’s standard MCMC algorithm. This paper analytically shows that the TA and SWA generally sample from different distributions, thereby…

得分驱动模型的最大似然估计AI 解读

We establish strong consistency and asymptotic normality of the maximum likelihood estimator for stochastic time-varying parameter models driven by the score of the predictive conditional likelihood function. For this purpose, we formulate primitive conditions for global identification, invertibility, strong consistency, and asymptotic normality both under correct specification and misspecification of the model. A detailed illustration is provided for a conditional…