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随机化选择后的精确推断AI 解读

Summary We introduce a pivot for exact selective inference with randomization. Not only does our pivot lead to exact inference in Gaussian regression models, but it is also available in closed form. We reduce this problem to inference for a bivariate truncated Gaussian variable. By doing so, we give up some power that is achieved with approximate maximum likelihood estimation in Panigrahi & Taylor (2023). Yet our pivot always produces narrower confidence intervals than a…

错误发现比例中位数的灵活控制AI 解读

Summary We introduce a multiple testing procedure that controls the median of the proportion of false discoveries in a flexible way. The procedure requires only a vector of p-values as input and is comparable to the Benjamini–Hochberg method, which controls the mean of the proportion of false discoveries. Our method allows free choice of one or several values of $ \alpha $ after seeing the data, unlike the Benjamini–Hochberg procedure, which can be very anti-conservative…

算法辅助人类决策的最优策略AI 解读

Summary We consider optimal regimes for algorithm-assisted human decision-making. Such regimes are decision functions of measured pre-treatment variables and, by leveraging natural treatment values, enjoy a superoptimality property whereby they are guaranteed to outperform conventional optimal regimes. When there is unmeasured confounding, the benefit of using superoptimal regimes can be considerable. When there is no unmeasured confounding, superoptimal regimes are…

时间序列非参数回归中的差分协方差矩阵估计及其设定检验应用AI 解读

Summary Long-run covariance matrix estimation is the building block of time series inference. The corresponding difference-based estimator, which avoids detrending, has attracted considerable interest due to its robustness to both smooth and abrupt structural breaks and its competitive finite sample performance. However, existing methods mainly focus on estimators for the univariate process, while their direct and multivariate extensions for most linear models are…

多变量高斯时间序列偏相关系数的推断AI 解读

Abstract We derive an asymptotic joint distribution and novel covariance estimator for the partial correlations of a multivariate Gaussian time series under mild regularity conditions. Using our derived asymptotic distribution, we develop a Wald confidence interval and testing procedure for inference of individual partial correlations for time series data. Through simulation we demonstrate that our proposed confidence interval attains higher coverage rates and our testing…

双向交叉混合效应模型的维度增长渐近理论AI 解读

This paper presents asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators within a two-way crossed mixed effect model as the sizes of the rows, columns, and cells tend to infinity. Under very mild conditions which do not require the assumption of normality, the estimators are proven to be asymptotically normal, possessing a structured covariance matrix. The growth rate for the number of rows, columns, and cells is unrestricted,…

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…

不规则信号下的变点分析AI 解读

This paper considers the problem of testing and estimation of change point where signals after the change point can be highly irregular, which departs from the existing literature that assumes signals after the change point to be piecewise constant or vary smoothly. A two-step approach is proposed to effectively estimate the location of the change point. The first step consists of a preliminary estimation of the change point that allows us to obtain unknown parameters for…

不受维度限制的岭回归AI 解读

Random matrix theory has become a widely useful tool in high-dimensional statistics and theoretical machine learning. However, random matrix theory is largely focused on the proportional asymptotics in which the number of columns grows proportionally to the number of rows of the data matrix. This is not always the most natural setting in statistics where columns correspond to covariates and rows to samples. With the objective to move beyond the proportional asymptotics, we…

Testing the significance of a variable or group of variables X for predicting a response Y, given additional covariates Z, is a ubiquitous task in statistics. A simple but common approach is to specify a linear model, and then test whether the regression coefficient for X is nonzero. However, when the model is misspecified, the test may have poor power, for example, when X is involved in complex interactions, or lead to many false rejections. In this work, we study the…

随机线性观测下的含噪恢复：椭球约束下的精确极小极大速率AI 解读

Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear operator; an important special case is random design regression. We derive sharp rates of estimation for arbitrary compact elliptical parameter sets and demonstrate how they depend on the distribution of the random linear operator. Our…

多维凸回归：最小二乘估计量的次优性AI 解读

Under the usual nonparametric regression model with Gaussian errors, Least Squares Estimators (LSEs) over natural subclasses of convex functions are shown to be suboptimal for estimating a d-dimensional convex function in squared error loss when the dimension d is 5 or larger. The specific function classes considered include: (i) bounded convex functions supported on a polytope (in random design), (ii) Lipschitz convex functions supported on any convex domain (in random…

维度增长的非参数交互模型中的深度神经网络AI 解读

Deep neural networks have achieved tremendous success due to their representation power and adaptation to low-dimensional structures. Their potential for estimating structured regression functions has been recently established in the literature. However, most of the studies require the input dimension to be fixed and consequently ignore the effect of dimension on the rate of convergence and hamper their applications to modern big data with high dimensionality. In this paper,…

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偏斜 Bernstein–von Mises 定理与偏斜模态近似AI 解读

Gaussian deterministic approximations are routinely employed in Bayesian statistics to ease inference when the target posterior is intractable. Although these approximations are justified, in asymptotic regimes, by Bernstein-von Mises type results, in practice the expected Gaussian behavior might poorly represent the actual shape of the target posterior, thus affecting approximation accuracy. Motivated by these considerations, we derive an improved class of closed-form and…

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…

通过迭代投影估计张量因子模型AI 解读

Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to Tucker tensor decomposition, except that the time dimension is treated as a dynamic process with a time dependent structure. In this paper, we introduce two approaches to estimate such a tensor factor model by using iterative orthogonal…

张量对张量回归：黎曼优化、过参数化与统计计算鸿沟的相互作用AI 解读

We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without prior knowledge of its intrinsic rank. We propose the Riemannian gradient descent (RGD) and Riemannian Gauss–Newton (RGN) methods and cope with the challenge of unknown rank by studying the effect of rank over-parameterization. We provide the first convergence guarantee for the general tensor-on-tensor regression…

利用正则变差随机向量的凸组合估计谱测度AI 解读

The extremal dependence structure of a regularly varying random vector X is fully described by its limiting spectral measure. In this paper, we investigate how to recover characteristics of the measure, such as extremal coefficients, from the extremal behaviour of convex combinations of components of X. Our considerations result in a class of new estimators of moments of the corresponding combinations for the spectral vector. We show asymptotic normality by means of a…

非独立成分分析AI 解读

A seminal result in the ICA literature states that for AY=ε, if the components of ε are independent and at most one is Gaussian, then A is identified up to sign and permutation of its rows (Signal Process. 36 (1994)). In this paper we study to which extent the independence assumption can be relaxed by replacing it with restrictions on higher order moment or cumulant tensors of ε. We document new conditions that establish identification for several nonindependent component…

投资型资产定价模型的估计与检验AI 解读

Investment-based asset pricing models typically predict a close link between a firm’s stock return and its characteristics at any point in time. Yet, previous studies have primarily focused on the weaker prediction that this link holds on average, finding substantial empirical support. We show how to incorporate the time-series predictions in the estimation and testing of investment-based models using the generalized method of moments. We find that standard specifications of…

缺乏小阶有限矩的 GARCH-MIDAS 模型推断AI 解读

In GARCH-mixed-data sampling models, the volatility is decomposed into the product of two factors which are often interpreted as “short-run” (high-frequency) and “long-run” (low-frequency) components. While two-component volatility models are widely used in applied works, some of their theoretical properties remain unexplored. We show that the strictly stationary solutions of such models do not admit any small-order finite moment, contrary to classical GARCH. It is shown…

预测回归的新稳健推断方法AI 解读

We propose a robust inference method for predictive regression models under heterogeneously persistent volatility as well as endogeneity, persistence, or heavy-tailedness of regressors. This approach relies on two methodologies, nonlinear instrumental variable estimation and volatility correction, which are used to deal with the aforementioned characteristics of regressors and volatility, respectively. Our method is simple to implement and is applicable both in the case of…

含交互固定效应的核范数正则化分位数回归AI 解读

This paper studies large N and large T conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the interactive fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of) interactive fixed effects. It also allows the number of covariates to grow slowly with N and T . We derive an error…

非线性选择模型中的截距估计AI 解读

We propose various semiparametric estimators for nonlinear selection models, where slope and intercept can be separately identified. When the selection equation satisfies a monotonic index restriction, we suggest a local polynomial estimator, using only observations for which the marginal cumulative distribution function of the instrument index is close to one. Data-driven procedures such as cross-validation may be used to select the bandwidth for this estimator. We then…