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回归模型中随机效应的简单检验AI 解读

Testing that random effects are zero is difficult, because the null hypothesis restricts the corresponding variance parameter to the edge of the feasible parameter space. In the context of generalized linear mixed models, this paper exploits the link between random effects and penalized regression to develop a simple test for a zero effect. The idea is to treat the variance components not being tested as fixed at their estimates and then to express the likelihood ratio as a…

通过自适应核范数惩罚进行降秩回归AI 解读

We propose an adaptive nuclear norm penalization approach for low-rank matrix approximation, and use it to develop a new reduced rank estimation method for high-dimensional multivariate regression. The adaptive nuclear norm is defined as the weighted sum of the singular values of the matrix, and it is generally non-convex under the natural restriction that the weight decreases with the singular value. However, we show that the proposed non-convex penalized regression method…

右删失数据半参数变换模型中的变量选择AI 解读

We study variable selection in general transformation models for right-censored data. The models studied can incorporate external time-varying covariates, and they include the proportional hazards model and the proportional odds model as special cases. We propose an estimation method that involves minimizing a weighted negative partial loglikelihood function plus an adaptive lasso penalty, with the initial values obtained from nonparametric maximum likelihood estimation. The…

控制错误发现率的高斯图模型估计AI 解读

This paper studies the estimation of a high-dimensional Gaussian graphical model (GGM). Typically, the existing methods depend on regularization techniques. As a result, it is necessary to choose the regularized parameter. However, the precise relationship between the regularized parameter and the number of false edges in GGM estimation is unclear. In this paper we propose an alternative method by a multiple testing procedure. Based on our new test statistics for conditional…

高维稀疏主子空间估计的极小极大理论AI 解读

We study sparse principal components analysis in high dimensions, where $p$ (the number of variables) can be much larger than $n$ (the number of observations), and analyze the problem of estimating the subspace spanned by the principal eigenvectors of the population covariance matrix. We introduce two complementary notions of $\ell_{q}$ subspace sparsity: row sparsity and column sparsity. We prove nonasymptotic lower and upper bounds on the minimax subspace estimation error…

高维时间序列的协方差与精度矩阵估计AI 解读

We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus forming a covariance matrix function. Using the functional dependence measure of Wu [Proc. Natl. Acad. Sci. USA 102 (2005) 14150–14154 (electronic)], we obtain the rate of convergence for the thresholded estimate and illustrate how the…

稀疏回归中的置信集AI 解读

The problem of constructing confidence sets in the high-dimensional linear model with $n$ response variables and $p$ parameters, possibly $p\ge n$, is considered. Full honest adaptive inference is possible if the rate of sparse estimation does not exceed $n^{-1/4}$, otherwise sparse adaptive confidence sets exist only over strict subsets of the parameter spaces for which sparse estimators exist. Necessary and sufficient conditions for the existence of confidence sets that…

完全子集回归AI 解读

This paper proposes a new method for combining forecasts based on complete subset regressions. For a given set of potential predictor variables we combine forecasts from all possible linear regression models that keep the number of predictors fixed. We explore how the choice of model complexity, as measured by the number of included predictor variables, can be used to trade off the bias and variance of the forecast errors, generating a setup akin to the efficient frontier…

降秩惩罚样条平滑的边际方法及其多层函数数据应用AI 解读

Multilevel functional data is collected in many biomedical studies. For example, in a study of the effect of Nimodipine on patients with subarachnoid hemorrhage (SAH), patients underwent multiple 4-hour treatment cycles. Within each treatment cycle, subjects' vital signs were reported every 10 minutes. This data has a natural multilevel structure with treatment cycles nested within subjects and measurements nested within cycles. Most literature on nonparametric analysis of…

通过嵌套高斯过程实现局部自适应贝叶斯非参数回归AI 解读

We propose a nested Gaussian process (nGP) as a locally adaptive prior for Bayesian nonparametric regression. Specified through a set of stochastic differential equations (SDEs), the nGP imposes a Gaussian process prior for the function’s mth-order derivative. The nesting comes in through including a local instantaneous mean function, which is drawn from another Gaussian process inducing adaptivity to locally varying smoothness. We discuss the support of the nGP prior in…

流形上的局部线性回归及其几何解释AI 解读

High-dimensional data analysis has been an active area, and the main focus areas have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear manifold. Under this manifold assumption, one purpose of this article is regression and gradient estimation on the manifold, and another is developing a new tool for manifold learning. As regards the first aim, we suggest directly reducing…

含高维协变量的广义可加部分线性模型AI 解读

This paper studies generalized additive partial linear models with high-dimensional covariates. We are interested in which components (including parametric and nonparametric components) are nonzero. The additive nonparametric functions are approximated by polynomial splines. We propose a doubly penalized procedure to obtain an initial estimate and then use the adaptive least absolute shrinkage and selection operator to identify nonzero components and to obtain the final…

高维影响度量AI 解读

Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity may amplify both the chance of an observation being influential, and its potential impact on the analysis. In this article, we propose a novel high-dimensional influence measure for regressions with the number of predictors far exceeding the…

超高维非凸惩罚回归的校准AI 解读

We investigate high-dimensional non-convex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is…

高维半参数双图模型AI 解读

In multivariate analysis, a Gaussian bigraphical model is commonly used for modelling matrix-valued data. In this paper, we propose a semiparametric extension of the Gaussian bigraphical model, called the nonparanormal bigraphical model. A projected nonparametric rank-based regularization approach is employed to estimate sparse precision matrices and produce graphs under a penalized likelihood framework. Theoretically, our semiparametric procedure achieves the parametric…

半参数模型中的降维与预测变量选择AI 解读

Dimension reduction in semiparametric regressions includes construction of informative linear combinations and selection of contributing predictors. To reduce the predictor dimension in semiparametric regressions, we propose an ℓ1-minimization of sliced inverse regression with the Dantzig selector, and establish a non-asymptotic error bound for the resulting estimator. We also generalize the regularization concept to sliced inverse regression with an adaptive Dantzig…

惩罚样条两种框架下的平滑参数选择AI 解读

Summary There are two popular smoothing parameter selection methods for spline smoothing. First, smoothing parameters can be estimated by minimizing criteria that approximate the average mean-squared error of the regression function estimator. Second, the maximum likelihood paradigm can be employed, under the assumption that the regression function is a realization of some stochastic process. The asymptotic properties of both smoothing parameter estimators for penalized…

阈值化参数空间中正则化方法的渐近等价性AI 解读

High-dimensional data analysis has motivated a spectrum of regularization methods for variable selection and sparse modeling, with two popular methods being convex and concave ones. A long debate has taken place on whether one class dominates the other, an important question both in theory and to practitioners. In this article, we characterize the asymptotic equivalence of regularization methods, with general penalty functions, in a thresholded parameter space under the…

扩散加权成像数据中扩散张量的空间收缩估计AI 解读

Diffusion tensor imaging (DTI), based on the diffusion-weighted imaging (DWI) data acquired from magnetic resonance experiments, has been widely used to analyze the physical structure of white-matter fibers in the human brain in vivo. The raw DWI data, however, carry noise; this contaminates the diffusion tensor (DT) estimates and introduces systematic bias into the induced eigenvalues. These bias components affect the effectiveness of fiber-tracking algorithms. In this…

误设模型惩罚似然估计中正则化参数选择的效率AI 解读

It has been shown that Akaike information criterion (AIC)-type criteria are asymptotically efficient selectors of the tuning parameter in nonconcave penalized regression methods under the assumption that the population variance is known or that a consistent estimator is available. We relax this assumption to prove that AIC itself is asymptotically efficient and we study its performance in finite samples. In classical regression, it is known that AIC tends to select overly…

部分因子建模：线性回归中依赖预测变量的收缩AI 解读

We develop a modified Gaussian factor model for the purpose of inducing predictor-dependent shrinkage for linear regression. The new model predicts well across a wide range of covariance structures, on real and simulated data. Furthermore, the new model facilitates variable selection in the case of correlated predictor variables, which often stymies other methods.

用于文本分析的多项逆回归AI 解读

Text data, including speeches, stories, and other document forms, are often connected to sentiment variables that are of interest for research in marketing, economics, and elsewhere. It is also very high dimensional and difficult to incorporate into statistical analyses. This article introduces a straightforward framework of sentiment-sufficient dimension reduction for text data. Multinomial inverse regression is introduced as a general tool for simplifying predictor sets…

高维度对有限样本的影响AI 解读

High-dimensional data sets are commonly collected in many contemporary applications arising in various fields of scientific research. We present two views of finite samples in high dimensions: a probabilistic one and a nonprobabilistic one. With the probabilistic view, we establish the concentration property and robust spark bound for large random design matrix generated from elliptical distributions, with the former related to the sure screening property and the latter…

税收对增长的非线性影响：使用平均边际税率的半参数方法AI 解读

SUMMARY One of the major challenges of empirical tax research is the identification and calculation of appropriate tax data. While there is consensus that average marginal tax rates are most suitable for studying the effects of tax policy on economic growth, because of data limitations the calculation of marginal tax rates has been limited to the USA and the UK. This paper provides calculations of average marginal tax rates for the four Scandinavian countries using the…