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数据不共享条件下稀疏高维模型的协同推断AI 解读

In modern data analysis, an improvement in statistical efficiency is expected via effective collaboration among multiple data holders with non-shared data. In this article, we propose a collaborative score-type test (CST) for testing linear hypotheses, which accommodates potentially high-dimensional nuisance parameters and a diverging number of constraints and target parameters. Through a careful decomposition of the Kiefer-Bahadur representation for the traditional score…

主成分空间中的高维回归与维数增益：再考察AI 解读

Benefits of exploiting sparsity in the space of principal components have been well documented both empirically and theoretically (Lang and Zou; Silin and Fan). In this article, we further reveal another unexpected advantage of exploiting sparsity in the space of principal components when the data are contaminated by measurement errors. Assuming the coefficient vector resides in an lq ball (0≤q≤1), we show that an l1 penalized principal components regression has a prediction…

通过近似消息传递实现高维 Newey–Powell 检验AI 解读

We propose a high-dimensional extension of the heteroscedasticity test proposed in Newey and Powell (1987). Our test is based on expectile regression in the proportional asymptotic regime where $n/p \to \delta \in (0,1]$ . The asymptotic analysis of the test statistic uses the approximate message passing algorithm, from which we obtain the limiting distribution of the test and establish its asymptotic power. The numerical performance of the test is validated through an…

稀疏高斯化典型相关分析及其投资组合应用AI 解读

Canonical correlation analysis (CCA) is an important statistical technique that explores the linear relationships between two sets of variables. In this article, we propose a new generalization of CCA named sparse Gaussianized CCA (SGCCA) for high-dimensional data analysis. SGCCA has a number of favorable properties. First, it is conceptually easy to comprehend and efficient to implement. Second, it not only yields sparse and nested canonical vectors, but is also invariant…

通过包络正则化增强响应包络模型AI 解读

The response envelope model provides substantial efficiency gains over the standard multivariate linear regression by identifying the material part of the response to the model and by excluding the immaterial part. In this article, we propose the enhanced response envelope by incorporating a novel envelope regularization term based on a nonconvex manifold formulation. It is shown that the enhanced response envelope can yield better prediction risk than the original envelope…

包络 Huber 回归AI 解读

Huber regression (HR) is a popular flexible alternative to the least squares regression when the error follows a heavy-tailed distribution. We propose a new method called the enveloped Huber regression (EHR) by considering the envelope assumption that there exists some subspace of the predictors that has no association with the response, which is referred to as the immaterial part. More efficient estimation is achieved via the removal of the immaterial part. Different from…

高维稀疏卷积秩回归AI 解读

Wang et al. studied the high-dimensional sparse penalized rank regression and established its nice theoretical properties. Compared with the least squares, rank regression can have a substantial gain in estimation efficiency while maintaining a minimal relative efficiency of 86.4%. However, the computation of penalized rank regression can be very challenging for high-dimensional data, due to the highly nonsmooth rank regression loss. In this work we view the rank regression…

用于高维回归分析的非参数Box–Cox模型AI 解读

The mainstream theory for high-dimensional regression assumes that the underlying true model is a low-dimensional linear regression model. On the other hand, a standard technique in regression analysis, even in the traditional low-dimensional setting, is to employ the Box–Cox transformation for reducing anomalies such as non-additivity and heteroscedasticity in linear regression. In this paper, we propose a new high-dimensional regression method based on a nonparametric…

基于惩罚 Tobit 似然的高维删失回归AI 解读

High-dimensional regression and regression with a left-censored response are each well-studied topics. In spite of this, few methods have been proposed which deal with both of these complications simultaneously. The Tobit model—long the standard method for censored regression in economics—has not been adapted for high-dimensional regression at all. To fill this gap and bring up-to-date techniques from high-dimensional statistics to the field of high-dimensional left-censored…

利用交叉拟合残差回归识别高维异方差效应AI 解读

There is a vast amount of work on high-dimensional regression. The common starting point for the existing theoretical work is to assume the data generating model is a homoscedastic linear regression model with some sparsity structure. In reality the homoscedasticity assumption is often violated, and hence understanding the heteroscedasticity of the data is of critical importance. In this article we systematically study the estimation of a high-dimensional heteroscedastic…

重新审视距离加权判别AI 解读

Summary Distance-weighted discrimination (DWD) is a modern margin-based classifier with an interesting geometric motivation. It was proposed as a competitor to the support vector machine (SVM). Despite many recent references on DWD, DWD is far less popular than the SVM, mainly because of computational and theoretical reasons. We greatly advance the current DWD methodology and its learning theory. We propose a novel thrifty algorithm for solving standard DWD and generalized…

CoCoLasso：协变量含测量误差的高维回归AI 解读

Much theoretical and applied work has been devoted to high-dimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright [Ann. Statist. 40 (2012) 1637–1664] proposed a nonconvex modification of the Lasso for doing high-dimensional regression with noisy and missing data. It is generally agreed that the virtues of convexity contribute fundamentally the success…

混合数据的高维半参数潜在图模型AI 解读

Summary We propose a semiparametric latent Gaussian copula model for modelling mixed multivariate data, which contain a combination of both continuous and binary variables. The model assumes that the observed binary variables are obtained by dichotomizing latent variables that satisfy the Gaussian copula distribution. The goal is to infer the conditional independence relationship between the latent random variables, based on the observed mixed data. Our work has two main…

非对称最小二乘回归的高维推广及其应用AI 解读

Asymmetric least squares regression is an important method that has wide applications in statistics, econometrics and finance. The existing work on asymmetric least squares only considers the traditional low dimension and large sample setting. In this paper, we systematically study the Sparse Asymmetric LEast Squares (SALES) regression under high dimensions where the penalty functions include the Lasso and nonconvex penalties. We develop a unified efficient algorithm for…

transnormal 模型下的多任务分位数回归AI 解读

We consider estimating multitask quantile regression under the transnormal model, with focus on high-dimensional setting. We derive a surprisingly simple closed-form solution through rank-based covariance regularization. In particular, we propose the rank-based ℓ1 penalization with positive-definite constraints for estimating sparse covariance matrices, and the rank-based banded Cholesky decomposition regularization for estimating banded precision matrices. By taking…

融合 Kolmogorov 筛选器：非参数无模型变量筛选方法AI 解读

A new model-free screening method called the fused Kolmogorov filter is proposed for high-dimensional data analysis. This new method is fully nonparametric and can work with many types of covariates and response variables, including continuous, discrete and categorical variables. We apply the fused Kolmogorov filter to deal with variable screening problems emerging from a wide range of applications, such as multiclass classification, nonparametric regression and Poisson…

折叠凹惩罚估计的强 oracle 最优性AI 解读

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To…

大型协方差矩阵的正定 ℓ1 惩罚估计AI 解读

The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To fix this drawback of thresholding estimation, we develop a positive-definite ℓ1-penalized covariance estimator for estimating sparse large covariance matrices. We derive an efficient alternating direction method to solve the challenging optimization problem and establish its convergence…

高维非正态变换图模型的正则化秩估计AI 解读

A sparse precision matrix can be directly translated into a sparse Gaussian graphical model under the assumption that the data follow a joint normal distribution. This neat property makes high-dimensional precision matrix estimation very appealing in many applications. However, in practice we often face nonnormal data, and variable transformation is often used to achieve normality. In this paper we consider the nonparanormal model that assumes that the variables follow a…

稀疏 Ising 模型的非凹惩罚复合条件似然估计AI 解读

The Ising model is a useful tool for studying complex interactions within a system. The estimation of such a model, however, is rather challenging, especially in the presence of high-dimensional parameters. In this work, we propose efficient procedures for learning a sparse Ising model based on a penalized composite conditional likelihood with nonconcave penalties. Nonconcave penalized likelihood estimation has received a lot of attention in recent years. However, such an…

半参数变系数部分线性模型的新型高效估计与变量选择方法AI 解读

The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the semiparametric varying-coefficient partially linear model. We first study quantile regression estimates for the nonparametric varying-coefficient functions and the parametric regression coefficients. To achieve nice efficiency properties, we…

局部复合分位数回归平滑：局部多项式回归的替代方法AI 解读

Summary Local polynomial regression is a useful non-parametric regression tool to explore fine data structures and has been widely used in practice. We propose a new non-parametric regression technique called local composite quantile regression smoothing to improve local polynomial regression further. Sampling properties of the estimation procedure proposed are studied. We derive the asymptotic bias, variance and normality of the estimate proposed. The asymptotic relative…

广义非线性 ℓ1 正则化解路径的高效全局近似及应用AI 解读

We consider efficient construction of nonlinear solution paths for general ℓ1-regularization. Unlike the existing methods that incrementally build the solution path through a combination of local linear approximation and recalibration, we propose an efficient global approximation to the whole solution path. With the loss function approximated by a quadratic spline, we show that the solution path can be computed using a generalized Lars algorithm. The proposed methodology…

参数维度随样本量增长时的自适应弹性网AI 解读

We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property (Fan and Li, 2001; Fan and Peng, 2004) which ensures the optimal large sample performance. Furthermore, the high-dimensionality often induces the collinearity problem which should be properly handled by the ideal method. Many existing variable selection methods fail to…