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通过维度扩展建模非平稳空间过程AI 解读

In this article, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher-dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multidimensional scaling, group lasso, and latent variable models, a dimensionally sparse projection is found in which the originally nonstationary field exhibits…

基于似然的变量选择与精确参数估计AI 解读

In high-dimensional data analysis, feature selection becomes one means for dimension reduction, which proceeds with parameter estimation. Concerning accuracy of selection and estimation, we study nonconvex constrained and regularized likelihoods in the presence of nuisance parameters. Theoretically, we show that constrained L(0)-likelihood and its computational surrogate are optimal in that they achieve feature selection consistency and sharp parameter estimation, under one…

依赖高维数据的跨维度推断AI 解读

A growing number of modern scientific problems in areas such as genomics, neurobiology, and spatial epidemiology involve the measurement and analysis of thousands of related features that may be stochastically dependent at arbitrarily strong levels. In this work, we consider the scenario where the features follow a multivariate Normal distribution. We demonstrate that dependence is manifested as random variation shared among features, and that standard methods may yield…

条件图模型的稀疏估计及其基因网络应用AI 解读

In many applications the graph structure in a network arises from two sources: intrinsic connections and connections due to external effects. We introduce a sparse estimation procedure for graphical models that is capable of isolating the intrinsic connections by removing the external effects. Technically, this is formulated as a conditional graphical model, in which the external effects are modeled as predictors, and the graph is determined by the conditional precision…

多元无序分类数据的单纯形因子模型AI 解读

Gaussian latent factor models are routinely used for modeling of dependence in continuous, binary, and ordered categorical data. For unordered categorical variables, Gaussian latent factor models lead to challenging computation and complex modeling structures. As an alternative, we propose a novel class of simplex factor models. In the single-factor case, the model treats the different categorical outcomes as independent with unknown marginals. The model can characterize…

基于高维特征筛选子集的偏差校正层级贝叶斯分类AI 解读

Class prediction based on high-dimensional features has received a great deal of attention in many areas of application. For example, biologists are interested in using microarray gene expression profiles for diagnosis or prognosis of a certain disease (e.g., cancer). For computational and other reasons, it is necessary to select a subset of features before fitting a statistical model, by evaluating how strongly the features are related to the response. However, such a…

相关性的检测AI 解读

We consider the hypothesis testing problem of deciding whether an observed high-dimensional vector has independent normal components or, alternatively, if it has a small subset of correlated components. The correlated components may have a certain combinatorial structure known to the statistician. We establish upper and lower bounds for the worst-case (minimax) risk in terms of the size of the correlated subset, the level of correlation, and the structure of the class of…

由支持函数估计凸集的最优收敛率AI 解读

We present a minimax optimal solution to the problem of estimating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regularizations of the least squares estimator. Both fixed and random designs are considered.

信息密集型高维回归中的预测变量充分降维估计AI 解读

We study the asymptotic behavior of a class of methods for sufficient dimension reduction in high-dimension regressions, as the sample size and number of predictors grow in various alignments. It is demonstrated that these methods are consistent in a variety of settings, particularly in abundant regressions where most predictors contribute some information on the response, and oracle rates are possible. Simulation results are presented to support the theoretical conclusion.

存在潜在变量与选择变量时的高维有向无环图学习AI 解读

We consider the problem of learning causal information between random variables in directed acyclic graphs (DAGs) when allowing arbitrarily many latent and selection variables. The FCI (Fast Causal Inference) algorithm has been explicitly designed to infer conditional independence and causal information in such settings. However, FCI is computationally infeasible for large graphs. We therefore propose the new RFCI algorithm, which is much faster than FCI. In some situations…

UPS 实现高维变量选择的最优相图AI 解读

Consider a linear model Y = Xβ + z, z ∼ N(0, In). Here, X = Xn,p, where both p and n are large, but p > n. We model the rows of X as i.i.d. samples from N(0, 1/n Ω), where Ω is a p × p correlation matrix, which is unknown to us but is presumably sparse. The vector β is also unknown but has relatively few nonzero coordinates, and we are interested in identifying these nonzeros. We propose the Univariate Penalization Screeing (UPS) for variable selection. This is a screen and…

超高维回归中基于重拟合交叉验证的方差估计AI 解读

Summary Variance estimation is a fundamental problem in statistical modelling. In ultrahigh dimensional linear regression where the dimensionality is much larger than the sample size, traditional variance estimation techniques are not applicable. Recent advances in variable selection in ultrahigh dimensional linear regression make this problem accessible. One of the major problems in ultrahigh dimensional regression is the high spurious correlation between the unobserved…

非零阈值 Tobit 模型中的聚焦信息准则、模型选择与模型平均AI 解读

Claeskens and Hjort (2003) have developed a focused information criterion (FIC) for model selection that selects different models based on different focused functions with those functions tailored to the parameters singled out for interest. Hjort and Claeskens (2003) also have presented model averaging as an alternative to model selection, and suggested a local misspecification framework for studying the limiting distributions and asymptotic risk properties of post-model…

非单调无应答面板数据中不可忽略缺失的影响评估AI 解读

SUMMARY The analysis of panel data with non‐monotone nonresponse often relies on the critical and untestable assumption of ignorable missingness. It is important to assess the consequences of departures from the ignorability assumption. Non‐monotone nonresponse, however, can often make such sensitivity analysis infeasible because the likelihood functions for alternative models involve high‐dimensional and difficult‐to‐evaluate integrals with respect to missing outcomes. We…

最优工具变量的稀疏模型与方法：征收权应用AI 解读

We develop results for the use of LASSO and Post-LASSO methods to form firststage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p, that apply even when p is much larger than the sample size, n.We rigorously develop asymptotic distribution and inference theory for the resulting IV estimators and provide conditions under which these estimators are asymptotically oracle-efficient.In simulation experiments, the…

结构分位数效应的非参数工具变量估计AI 解读

We study the asymptotic distribution of Tikhonov Regularized estimation of quantile structural effects implied by a nonseparable model. The nonparametric instrumental variable estimator is based on a minimum distance principle. We show that the minimum distance problem without regularization is locally ill-posed, and consider penalization by the norms of the parameter and its derivatives. We derive pointwise asymptotic normality and develop a consistent estimator of the…

广义残差可能不光滑的非参数条件矩模型估计AI 解读

This paper studies nonparametric estimation of conditional moment restrictions in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estimators, which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the…

平方根 lasso：通过锥规划实现枢轴式稀疏信号恢复AI 解读

We propose a pivotal method for estimating high-dimensional sparse linear regression models, where the overall number of regressors p is large, possibly much larger than n, but only s regressors are significant. The method is a modification of the lasso, called the square-root lasso. The method is pivotal in that it neither relies on the knowledge of the standard deviation σ nor does it need to pre-estimate σ. Moreover, the method does not rely on normality or…

协方差矩阵的稀疏估计AI 解读

We suggest a method for estimating a covariance matrix on the basis of a sample of vectors drawn from a multivariate normal distribution. In particular, we penalize the likelihood with a lasso penalty on the entries of the covariance matrix. This penalty plays two important roles: it reduces the effective number of parameters, which is important even when the dimension of the vectors is smaller than the sample size since the number of parameters grows quadratically in the…

变异函数及其谱的非参数估计AI 解读

In the study of intrinsically stationary spatial processes, a new nonparametric variogram estimator is proposed through its spectral representation. The methodology is based on estimation of the variogram’s spectrum by solving a regularized inverse problem through quadratic programming. The estimated variogram is guaranteed to be conditionally negative-definite. Simulation shows that our estimator is flexible and generally has smaller mean integrated squared error than the…

高维时间序列潜在因子的估计AI 解读

This paper deals with the dimension reduction of high-dimensional time series based on a lower-dimensional factor process. In particular, we allow the dimension of time series N to be as large as, or even larger than, the length of observed time series T. The estimation of the factor loading matrix and the factor process itself is carried out via an eigenanalysis of a N×N non-negative definite matrix. We show that when all the factors are strong in the sense that the norm of…

大维协方差矩阵估计的前向自适应带状化AI 解读

We propose a simple forward adaptive banding method for estimating large covariance matrices using the modified Cholesky decomposition. This approach requires the fitting of a prespecified set of models due to the adaptive banding structure and can be efficiently implemented. Aside from its computational attractiveness, we propose a novel Bayes information criterion that gives consistent model selection for estimating high dimensional covariance matrices. The method compares…

Wishart 分布混合的极小极大估计AI 解读

The space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference. Many books and papers have been written on this subject, and more recently there has been considerable interest in high-dimensional random matrices with particular emphasis on the distribution of certain eigenvalues. With the availability of modern data acquisition…

近似因子模型中的高维协方差矩阵估计AI 解读

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By…