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稀疏超高维变系数模型中的非参数独立筛选AI 解读

The varying-coefficient model is an important nonparametric statistical model that allows us to examine how the effects of covariates vary with exposure variables. When the number of covariates is big, the issue of variable selection arrives. In this paper, we propose and investigate marginal nonparametric screening methods to screen variables in ultra-high dimensional sparse varying-coefficient models. The proposed nonparametric independence screening (NIS) selects…

结合扩展贝叶斯信息准则的序贯 Lasso 超高维特征选择AI 解读

In this article, we propose a method called sequential Lasso (SLasso) for feature selection in sparse high-dimensional linear models. The SLasso selects features by sequentially solving partially penalized least squares problems where the features selected in earlier steps are not penalized. The SLasso uses extended BIC (EBIC) as the stopping rule. The procedure stops when EBIC reaches a minimum. The asymptotic properties of SLasso are considered when the dimension of the…

模型选择后的估计与精度评估AI 解读

Classical statistical theory ignores model selection in assessing estimation accuracy. Here we consider bootstrap methods for computing standard errors and confidence intervals that take model selection into account. The methodology involves bagging, also known as bootstrap smoothing, to tame the erratic discontinuities of selection-based estimators. A useful new formula for the accuracy of bagging then provides standard errors for the smoothed estimators. Two examples,…

基于惩罚样条与狄利克雷过程混合的贝叶斯非参数工具变量回归AI 解读

We propose a Bayesian nonparametric instrumental variable approach under additive separability that allows us to correct for endogeneity bias in regression models where the covariate effects enter with unknown functional form. Bias correction relies on a simultaneous equations specification with flexible modeling of the joint error distribution implemented via a Dirichlet process mixture prior. Both the structural and instrumental variable equation are specified in terms of…

高维带状精度矩阵带宽识别的假设检验AI 解读

Many statistical analysis procedures require a good estimator for a high-dimensional covariance matrix or its inverse, the precision matrix. When the precision matrix is banded, the Cholesky-based method often yields a good estimator of the precision matrix. One important aspect of this method is determination of the band size of the precision matrix. In practice, crossvalidation is commonly used; however, we show that crossvalidation not only is computationally intensive…

高维线性模型中的方差估计AI 解读

The residual variance and the proportion of explained variation are important quantities in many statistical models and model fitting procedures. They play an important role in regression diagnostics and model selection procedures, as well as in determining the performance limits in many problems. In this paper we propose new method-of-moments-based estimators for the residual variance, the proportion of explained variation and other related quantities, such as the ℓ2 signal…

超高维数据中样本特征值、特征向量与主成分得分的收敛AI 解读

The development of high-throughput biomedical technologies has led to increased interest in the analysis of high-dimensional data where the number of features is much larger than the sample size. In this paper, we investigate principal component analysis under the ultra-high dimensional regime, where both the number of features and the sample size increase as the ratio of the two quantities also increases. We bridge the existing results from the finite and the high-dimension…

高维阈值回归与收缩效应AI 解读

Summary High dimensional sparse modelling via regularization provides a powerful tool for analysing large-scale data sets and obtaining meaningful interpretable models. The use of non-convex penalty functions shows advantage in selecting important features in high dimensions, but the global optimality of such methods still demands more understanding. We consider sparse regression with a hard thresholding penalty, which we show to give rise to thresholded regression. This…

再生核希尔伯特空间中的结构化函数型加性回归AI 解读

Summary Functional additive models provide a flexible yet simple framework for regressions involving functional predictors. The utilization of a data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting non-linear additive components has been less studied. In this work, we propose a new regularization framework for structure estimation in the context of reproducing kernel…

高维模型中渐近最优的置信区域与检验AI 解读

We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking dependence among tests into account. For linear models, our method is essentially the same as in Zhang and Zhang [J. R. Stat. Soc. Ser. B Stat. Methodol. 76 (2014) 217–242]: we analyze its asymptotic properties and establish its asymptotic…

超大协方差矩阵稀疏贝叶斯因子模型的后验收缩AI 解读

Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of posterior convergence rates in inferring high-dimensional covariance matrices where the dimension can be larger than the sample size. Under relevant sparsity assumptions on the true covariance matrix, we show that commonly-used point mass mixture…

高维模型中的内生性AI 解读

Most papers on high-dimensional statistics are based on the assumption that none of the regressors are correlated with the regression error, namely, they are exogenous. Yet, endogeneity can arise incidentally from a large pool of regressors in a high-dimensional regression. This causes the inconsistency of the penalized least-squares method and possible false scientific discoveries. A necessary condition for model selection consistency of a general class of penalized…

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…

高维非平稳时间序列的广义动态半参数因子模型AI 解读

High‐dimensional non‐stationary time series, which reveal both complex trends and stochastic behaviour, occur in many scientific fields, e.g. macroeconomics, finance, neuroeconomics, etc. To model these, we propose a generalized dynamic semi‐parametric factor model with a two‐step estimation procedure. After choosing smoothed functional principal components as space functions (factor loadings), we extract various temporal trends by employing variable selection techniques for…

维数增长下弯曲指数族的后验推断AI 解读

In this paper, we study the large‐sample properties of the posterior‐based inference in the curved exponential family under increasing dimensions. The curved structure arises from the imposition of various restrictions on the model, such as moment restrictions, and plays a fundamental role in econometrics and others branches of data analysis. We establish conditions under which the posterior distribution is approximately normal, which in turn implies various good properties…

自适应非参数工具变量估计：正则化参数的经验选择AI 解读

In nonparametric instrumental variables estimation, the mapping that identifies the function of interest, g, is discontinuous and must be regularized to permit consistent estimation. The optimal regularization parameter depends on population characteristics that are unknown in applications. This paper presents a theoretically justified empirical method for choosing the regularization parameter in series estimation. The method adapts to the unknown smoothness of g and other…

通过正则化多分量回归重建源汇关系：北海鳕鱼幼体迁移应用AI 解读

The problem of reconstructing the source-sink dynamics arises in many biological systems. Our research is motivated by marine applications where newborns are passively dispersed by ocean currents from several potential spawning sources to settle in various nursery regions that collectively constitute the sink. The reconstruction of the sparse source-sink linkage pattern, that is, to identify which sources contribute to which regions in the sink, is a challenging task in…

出生队列生育率的贝叶斯预测AI 解读

There are signs that fertility in rich countries may have stopped declining, but this depends critically on whether women currently in reproductive ages are postponing or reducing lifetime fertility. Analysis of average completed family sizes requires forecasts of remaining fertility for women born 1970–1995. We propose a Bayesian model for fertility that incorporates a priori information about patterns over age and time. We use a new dataset, the Human Fertility Database…

通过惩罚似然选择混合 Copula 模型AI 解读

A fundamental issue of applying a copula method in applications is how to choose an appropriate copula function for a given problem. In this article we address this issue by proposing a new copula selection approach via penalized likelihood plus a shrinkage operator. The proposed method selects an appropriate copula function and estimates the related parameters simultaneously. We establish the asymptotic properties of the proposed penalized likelihood estimator, including…

采用平方根降温的模拟随机逼近退火全局优化AI 解读

Simulated annealing has been widely used in the solution of optimization problems. As known by many researchers, the global optima cannot be guaranteed to be located by simulated annealing unless a logarithmic cooling schedule is used. However, the logarithmic cooling schedule is so slow that no one can afford to use this much CPU time. This article proposes a new stochastic optimization algorithm, the so-called simulated stochastic approximation annealing algorithm, which…

自适应多变量整体检验AI 解读

We present a methodology for dealing with recent challenges in testing global hypotheses using multivariate observations. The proposed tests target situations, often arising in emerging applications of neuroimaging, where the sample size n is relatively small compared with the observations’ dimension K. We employ adaptive designs allowing for sequential modifications of the test statistics adapting to accumulated data. The adaptations are optimal in the sense of maximizing…

大量高维随机向量之间的独立性检验AI 解读

Capturing dependence among a large number of high-dimensional random vectors is a very important and challenging problem. By arranging n random vectors of length p in the form of a matrix, we develop a linear spectral statistic of the constructed matrix to test whether the n random vectors are independent or not. Specifically, the proposed statistic can also be applied to n random vectors, each of whose elements can be written as either a linear stationary process or a…

EMVS：基于 EM 算法的贝叶斯变量选择AI 解读

Despite rapid developments in stochastic search algorithms, the practicality of Bayesian variable selection methods has continued to pose challenges. High-dimensional data are now routinely analyzed, typically with many more covariates than observations. To broaden the applicability of Bayesian variable selection for such high-dimensional linear regression contexts, we propose EMVS, a deterministic alternative to stochastic search based on an EM algorithm which exploits a…

结构突变时间序列的组 LASSOAI 解读

Consider a structural break autoregressive (SBAR) process where j = 1, …, m + 1, {t1, …, tm} are change-points, 1 = t0 < t1 < ⋅⋅⋅ < tm + 1 = n + 1, σ( · ) is a measurable function on , and {ϵt} are white noise with unit variance. In practice, the number of change-points m is usually assumed to be known and small, because a large m would involve a huge amount of computational burden for parameters estimation. By reformulating the problem in a variable selection context, the…