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物理引导的统计数据融合：重建海洋涡旋三维流场AI 解读

Accurate reconstruction of three-dimensional ocean current fields is critical for understanding ocean dynamics and real-time conduct of modern oceanographic field campaigns, particularly for mesoscale eddy surveys. We propose a physics-guided modeling and learning framework for multi-source data fusion to estimate the three-dimensional (3D) current structure of oceanic eddies by integrating satellite altimetry and temperature data, ocean reanalysis data, and in situ drifting…

基于极小极大缺损的高维假设最优自适应检验AI 解读

The detection boundary is a tool for power evaluation of a high dimensional test, which provides a binary phase transition of power in terms of signal density and strength. However, it cannot separate the L2 and higher criticism (HC) tests under dense signals, and the L∞ and HC tests under highly sparse signals as they share the same detection boundary. This paper proposes minimax relative deficiency and minimax absolute deficiency as sharper measures for power evaluation…

适用于一般损失函数的灵活差分隐私学习AI 解读

This paper aims to provide a versatile privacy-preserving release mechanism along with a unified approach for subsequent parameter estimation and statistical inference. We propose a privacy mechanism based on zero-inflated symmetric multivariate Laplace (ZIL) noise, which requires no prior specification of subsequent analysis tasks, allows for general loss functions under minimal conditions, imposes no limit on the number of analyses, and is adaptable to increasing data…

用于高斯近似的自归一化 Cramér 型中等偏差定理AI 解读

Berry–Esseen type bounds for Gaussian approximation of standardized sums have been extensively studied under exponential type moment conditions. In this paper, a Cramér type moderate deviation theorem is established for self-normalized Gaussian approximation under finite moment conditions. More specifically, let X1,X2,…,Xn be i.i.d. Rp-valued random vectors with zero means. Let Sn,j=∑ i=1nXij and Vn,j2=∑i=1nXij2. We show that if the correlation matrix of X1 is Ip and the…

去中心化联邦学习的统计推断AI 解读

This paper considers decentralized Federated Learning (FL) under heterogeneous distributions among distributed clients or data blocks for the M-estimation. The mean squared error and consensus error across the estimators from different clients via the decentralized stochastic gradient descent algorithm are derived. The asymptotic normality of the Polyak–Ruppert (PR) averaged estimator in the decentralized distributed setting is attained, which shows that its statistical…

四区制分段回归模型的统计推断AI 解读

Segmented regression models offer model flexibility and interpretability as compared to the global parametric and the nonparametric models, and yet are challenging in both estimation and inference. We consider a four-regime segmented model for temporally dependent data with segmenting boundaries depending on multivariate covariates with nondiminishing boundary effects. A mixed integer quadratic programming algorithm is formulated to facilitate the least square estimation of…

用于评估自回归过程处理效应的动态合成控制法AI 解读

Abstract Motivated by evaluating the effects of air pollution alerts on air quality, we propose the dynamic synthetic control method for micro-level data with time-varying confounders and spatial dependence under an auto-regressive model setting. We employ the empirical likelihood to define the synthetic control weights, which ensures a unique solution and permits theoretical analysis. The dynamic matching increases the feasibility of matching and enables us to assess the…

稀疏信号下高维协方差检验的精确最优性AI 解读

This paper considers one-sample testing of a high-dimensional covariance matrix by deriving the detection boundary as a function of the signal sparsity and signal strength under the sparse alternative hypotheses. It first shows that the optimal detection boundary for testing sparse means is the minimax detection lower boundary for testing the covariance matrix. A multilevel thresholding test is proposed and is shown to be able to attain the detection lower boundary over a…

多层阈值法下的两样本高维协方差检验与信号识别AI 解读

The paper considers testing and signal identification for covariance matrices from two populations of marginally sub-Gaussian distributed. A multi-level thresholding procedure is proposed for testing the equality of two high-dimensional covariance matrices, which is designed to detect sparse and faint differences between the covariances. A novel U-statistic composition is developed to establish the asymptotic distribution of the thresholding statistics in conjunction with…

海量数据的分布式统计推断AI 解读

This paper considers distributed statistical inference for general symmetric statistics in the context of massive data with efficient computation. Estimation efficiency and asymptotic distributions of the distributed statistics are provided, which reveal different results between the nondegenerate and degenerate cases, and show the number of the data subsets plays an important role. Two distributed bootstrap methods are proposed and analyzed to approximation the underlying…

高维经验似然推断AI 解读

Summary High-dimensional statistical inference with general estimating equations is challenging and remains little explored. We study two problems in the area: confidence set estimation for multiple components of the model parameters, and model specifications tests. First, we propose to construct a new set of estimating equations such that the impact from estimating the high-dimensional nuisance parameters becomes asymptotically negligible. The new construction enables us to…

高维均值的两样本与 ANOVA 检验AI 解读

This paper considers testing the equality of two high dimensional means. Two approaches are utilized to formulate $L_{2}$-type tests for better power performance when the two high dimensional mean vectors differ only in sparsely populated coordinates and the differences are faint. One is to conduct thresholding to remove the nonsignal bearing dimensions for variance reduction of the test statistics. The other is to transform the data via the precision matrix for signal…

结合协变量信息的矩阵补全AI 解读

This article investigates the problem of matrix completion from the corrupted data, when the additional covariates are available. Despite being seldomly considered in the matrix completion literature, these covariates often provide valuable information for completing the unobserved entries of the high-dimensional target matrix A0. Given a covariate matrix X with its rows representing the row covariates of A0, we consider a column-space-decomposition model A0 = Xβ0 + B0,…

通过阈值化极大似然估计检测稀少且微弱的信号AI 解读

Motivated by the analysis of RNA sequencing (RNA-seq) data for genes differentially expressed across multiple conditions, we consider detecting rare and faint signals in high-dimensional response variables. We address the signal detection problem under a general framework, which includes generalized linear models for count-valued responses as special cases. We propose a test statistic that carries out a multi-level thresholding on maximum likelihood estimators (MLEs) of the…

利用债券价格改进利率扩散模型的参数估计AI 解读

We consider improving estimating parameters of diffusion processes for interest rates by incorporating information in bond prices. This is designed to improve the estimation of the drift parameters, which are known to be subject to large estimation errors. It is shown that having the bond prices together with the short rates leads to more efficient estimation of all parameters for the interest rate models. It enhances the estimation efficiency of the maximum likelihood…

高维广义线性模型的检验AI 解读

Summary We consider testing regression coefficients in high dimensional generalized linear models. By modifying the test statistic of Goeman and his colleagues for large but fixed dimensional settings, we propose a new test, based on an asymptotic analysis, that is applicable for diverging dimensions and is robust to accommodate a wide range of link functions. The power properties of the tests are evaluated asymptotically under two families of alternative hypotheses. In…

Peter Hall 对自助法的贡献AI 解读

Professor Peter Hall's first publication appeared in 1977, one year after he was awarded DPhil from the University of Oxford and MSc from the Australian National University (ANU).His first paper on the bootstrap appeared in 1985[Hall (1985))] on the block bootstrap of spatial point patterns, six years after the seminal paper [Efron (1979)] that introduced the bootstrap method.Hall (1985) was his 103rd publication and proposed resampling "tiles" of spatial data ("coverage…

高维协方差矩阵超对角线结构的检验AI 解读

The covariance matrices are essential quantities in econometric and statistical applications including portfolio allocation, asset pricing and factor analysis. Testing the entire covariance under high dimensionality endures large variability and causes a dilution of the signal-to-noise ratio and hence a reduction in the power. We consider a more powerful test procedure that focuses on testing along the super-diagonals of the high dimensional covariance matrix, which can…

高维协方差矩阵估计的带宽选择AI 解读

Yumou Qiu & Song Xi ChenYumou Qiu is Assistant Professor, Department of Statistics, University of Nebraska-Lincoln, NE 68583-0963 (E-mail: ). Song Xi Chen is Chair Professor, Department of Business Statistics and Econometrics, Guanghua School of Management and Center for Statistical Science, Peking University, Beijing 100651, China, and Professor, Department of Statistics, Iowa State University, Ames, IA 50011-1210 (E-mail: ).We thank the editors, the AE and three anonymous…

弱依赖数据下高维矩约束的广义经验似然AI 解读

This paper considers the maximum generalized empirical likelihood (GEL) estimation and inference on parameters identified by high dimensional moment restrictions with weakly dependent data when the dimensions of the moment restrictions and the parameters diverge along with the sample size. The consistency with rates and the asymptotic normality of the GEL estimator are obtained by properly restricting the growth rates of the dimensions of the parameters and the moment…

期权隐含波动率：微笑成因与误差校正AI 解读

We analyze the properties of the implied volatility, the commonly used volatility estimator by direct option price inversion. It is found that the implied volatility is subject to a systematic bias in the presence of pricing errors, which makes it inconsistent to the underlying volatility. We propose an estimator of the underlying volatility by first estimating nonparametrically the option price function, followed by inverting the nonparametrically estimated price. It is…

稀疏与列间依赖下高维均值检验的 Higher Criticism 替代方法AI 解读

We consider two alternative tests to the Higher Criticism test of Donoho and Jin [Ann. Statist. 32 (2004) 962–994] for high-dimensional means under the sparsity of the nonzero means for sub-Gaussian distributed data with unknown column-wise dependence. The two alternative test statistics are constructed by first thresholding $L_{1}$ and $L_{2}$ statistics based on the sample means, respectively, followed by maximizing over a range of thresholding levels to make the tests…

针对缺失值与观察性研究进行处理前变量调整的Mann–Whitney检验AI 解读

Summary The conventional Wilcoxon or Mann–Whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies. This is because the missingness of the outcomes or the participation in the treatments may depend on certain pretreatment variables. We propose an approach to adjust the Mann–Whitney test by correcting the potential bias via consistently estimating the conditional distributions of the outcomes given the…

高维协方差矩阵的带状性检验与带宽估计AI 解读

Motivated by the latest effort to employ banded matrices to estimate a high-dimensional covariance $\Sigma$, we propose a test for $\Sigma$ being banded with possible diverging bandwidth. The test is adaptive to the “large $p$, small $n$” situations without assuming a specific parametric distribution for the data. We also formulate a consistent estimator for the bandwidth of a banded high-dimensional covariance matrix. The properties of the test and the bandwidth estimator…