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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…

大型 DSGE 模型的因子分析AI 解读

SUMMARY We study the workings of the factor analysis of high‐dimensional data using artificial series generated from a large, multi‐sector dynamic stochastic general equilibrium (DSGE) model. The objective is to use the DSGE model as a laboratory that allows us to shed some light on the practical benefits and limitations of using factor analysis techniques on economic data. We explain in what sense the artificial data can be thought of having a factor structure, study the…

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…

高维稀疏线性回归的近乎最优极小极大估计量AI 解读

We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints ($\ell_q$ constraint with $0

固定或增长维度下的协方差矩阵检验AI 解读

Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in general, and tests for high-dimensional covariance in the literature usually depend on some special structure of the matrix. In this paper, we propose some empirical likelihood ratio tests for testing whether a covariance matrix equals a given…

高维正态分布经典似然比检验的中心极限定理AI 解读

For random samples of size $n$ obtained from $p$-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been extensively studied in multivariate analysis, and their limiting distributions under the null hypothesis were proved to be chi-square distributions as $n$ goes to infinity and $p$ remains fixed. In this paper, we consider the…

含测量误差的高维 Itô 过程稀疏波动率矩阵最优估计AI 解读

Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a high-dimensional Itô process observed with measurement errors at discrete time points. The minimax rate of convergence is established for estimating sparse volatility matrices. By combining the multi-scale and threshold approaches we construct a…

高维稀疏主成分的最优检测AI 解读

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to be NP-complete in general, and we describe a computationally efficient alternative test using convex relaxations. Our relaxation is also proved to detect sparse principal components at near optimal detection levels, and it performs well on…

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…

拍卖次序统计量估计方法的大样本性质AI 解读

For symmetric auctions, there is a close relationship between distributions of order statistics of bidders' valuations and observable bids that is often used to estimate or bound the valuation distribution, optimal reserve price, and other quantities of interest nonparametrically. However, we show that the functional mapping from distributions of order statistics to their parent distribution is, in general, not Lipschitz continuous and, therefore, introduces an irregularity…

利用方差—均值混合进行非高斯回归的数据增广AI 解读

We use the theory of normal variance-mean mixtures to derive a data-augmentation scheme for a class of common regularization problems. This generalizes existing theory on normal variance mixtures for priors in regression and classification. It also allows variants of the expectation-maximization algorithm to be brought to bear on a wider range of models than previously appreciated. We demonstrate the method on several examples, focusing on the case of binary logistic…

稀疏向量组的双层稀疏估计AI 解读

We consider estimating a sparse group of sparse normal mean vectors, based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their significant components, which can be performed by a fast algorithm. The resulting estimators are developed within a Bayesian framework and can be viewed as maximum a posteriori estimators. We establish their adaptive minimaxity over a wide range of sparse and dense settings. A…

用于功率谱估计的惩罚多元 Whittle 似然AI 解读

Nonparametric estimation procedures that can flexibly account for varying levels of smoothness among different functional parameters, such as penalized likelihoods, have been developed in a variety of settings. However, geometric constraints on power spectra have limited the development of such methods when estimating the power spectrum of a vector-valued time series. This article introduces a penalized likelihood approach to nonparametric multivariate spectral analysis…

快速二维 P 样条：三明治平滑器AI 解读

Summary We propose a fast penalized spline method for bivariate smoothing. Univariate P-spline smoothers are applied simultaneously along both co-ordinates. The new smoother has a sandwich form which suggested the name ‘sandwich smoother’ to a referee. The sandwich smoother has a tensor product structure that simplifies an asymptotic analysis and it can be fast computed. We derive a local central limit theorem for the sandwich smoother, with simple expressions for the…

微分几何最小角回归：稀疏广义线性模型方法AI 解读

Summary Sparsity is an essential feature of many contemporary data problems. Remote sensing, various forms of automated screening and other high throughput measurement devices collect a large amount of information, typically about few independent statistical subjects or units. In certain cases it is reasonable to assume that the underlying process generating the data is itself sparse, in the sense that only a few of the measured variables are involved in the process. We…

高维惩罚似然中的调节参数选择AI 解读

Summary Determining how to select the tuning parameter appropriately is essential in penalized likelihood methods for high dimensional data analysis. We examine this problem in the setting of penalized likelihood methods for generalized linear models, where the dimensionality of covariates p is allowed to increase exponentially with the sample size n. We propose to select the tuning parameter by optimizing the generalized information criterion with an appropriate model…

基于条件数正则化的协方差估计AI 解读

Summary Estimation of high dimensional covariance matrices is known to be a difficult problem, has many applications and is of current interest to the larger statistics community. In many applications including the so-called ‘large p, small n’ setting, the estimate of the covariance matrix is required to be not only invertible but also well conditioned. Although many regularization schemes attempt to do this, none of them address the ill conditioning problem directly. We…

多核学习的快速学习率：稀疏性与光滑性的权衡AI 解读

We investigate the learning rate of multiple kernel learning (MKL) with $\ell_{1}$ and elastic-net regularizations. The elastic-net regularization is a composition of an $\ell_{1}$-regularizer for inducing the sparsity and an $\ell_{2}$-regularizer for controlling the smoothness. We focus on a sparse setting where the total number of kernels is large, but the number of nonzero components of the ground truth is relatively small, and show sharper convergence rates than the…

自适应 LASSO 的 Oracle 分布收敛速率与自助法高阶改进AI 解读

Zou [J. Amer. Statist. Assoc. 101 (2006) 1418–1429] proposed the Adaptive LASSO (ALASSO) method for simultaneous variable selection and estimation of the regression parameters, and established its oracle property. In this paper, we investigate the rate of convergence of the ALASSO estimator to the oracle distribution when the dimension of the regression parameters may grow to infinity with the sample size. It is shown that the rate critically depends on the choices of the…

高维数据球形性检验的渐近功效AI 解读

This paper studies the asymptotic power of tests of sphericity against perturbations in a single unknown direction as both the dimensionality of the data and the number of observations go to infinity. We establish the convergence, under the null hypothesis and contiguous alternatives, of the log ratio of the joint densities of the sample covariance eigenvalues to a Gaussian process indexed by the norm of the perturbation. When the perturbation norm is larger than the phase…