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样条估计量的统一框架AI 解读

This article develops a unified framework to study the asymptotic properties of all periodic spline-based estimators, that is, of regression, penalized and smoothing splines. The explicit form of the periodic Demmler–Reinsch basis in terms of exponential splines allows the derivation of an expression for the asymptotic equivalent kernel on the real line for all spline estimators simultaneously. The corresponding bandwidth, which drives the asymptotic behaviour of spline…

二维流形上的空间回归模型AI 解读

We propose a regression model for data spatially distributed over general two-dimensional Riemannian manifolds. This is a generalized additive model with a roughness penalty term involving a differential operator computed over the non-planar domain. By virtue of a semiparametric framework, the model allows inclusion of space-varying covariate information. Estimation can be performed by conformally parameterizing the non-planar domain and then generalizing existing models for…

基于非参数经验贝叶斯与极大似然推断的高维分类AI 解读

We propose new nonparametric empirical Bayes methods for high-dimensional classification. Our classifiers are designed to approximate the Bayes classifier in a hypothesized hierarchical model, where the prior distributions for the model parameters are estimated nonparametrically from the training data. As is common with nonparametric empirical Bayes, the proposed classifiers are effective in high-dimensional settings even when the underlying model parameters are in fact…

高维部分函数型线性回归AI 解读

In modern experiments, functional and nonfunctional data are often encountered simultaneously when observations are sampled from random processes and high-dimensional scalar covariates. It is difficult to apply existing methods for model selection and estimation. We propose a new class of partially functional linear models to characterize the regression between a scalar response and covariates of both functional and scalar types. The new approach provides a unified and…

条件独立性的非参数贝叶斯推断AI 解读

In many application areas, a primary focus is on assessing evidence in the data refuting the assumption of independence of |$Y$| and |$X$| conditionally on |$Z$|⁠, with |$Y$| response variables, |$X$| predictors of interest, and |$Z$| covariates. Ideally, one would have methods available that avoid parametric assumptions, allow |$Y, X, Z$| to be random variables on arbitrary spaces with arbitrary dimension, and accommodate rapid consideration of different candidate…

用于工具变量选择的Lasso：一项复现研究AI 解读

Summary Recently, Lasso methods have been applied to economic questions. In a seminal paper, Belloni et al . ( Econometrica ; 80 (6): 2369–2429) make use of (post‐)Lasso for instrumental variable selection in a setting where the number of instruments p is large or might even exceed the number of observations n —a situation which is prevalent in many current applications. We replicate their simulation study with the statistical package R (R Development Core Team ( )) and,…

超高维部分线性可加分位数回归AI 解读

We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete picture of the conditional distribution of a response variable given high dimensional covariates. (2) The sparsity level is allowed to be different at different quantile levels. (3) The partially linear additive structure accommodates…

因子模型中的投影主成分分析AI 解读

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employees principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to high-dimensional factor analysis, the projection removes noise components. We show that the unobserved latent factors can be more accurately estimated than the conventional PCA if the projection is genuine, or more precisely, when the factor…

平稳与非平稳自回归中自适应 Lasso 的一致及保守模型选择AI 解读

We show that the adaptive Lasso is oracle efficient in stationary and nonstationary autoregressions. This means that it estimates parameters consistently, selects the correct sparsity pattern, and estimates the coefficients belonging to the relevant variables at the same asymptotic efficiency as if only these had been included in the model from the outset. In particular, this implies that it is able to discriminate between stationary and nonstationary autoregressions and it…

线性逆问题的正则化先验AI 解读

This paper proposes a new Bayesian approach for estimating, nonparametrically, functional parameters in econometric models that are characterized as the solution of a linear inverse problem. By using a Gaussian process prior we propose the posterior mean as an estimator and prove frequentist consistency of the posterior distribution. The latter provides the frequentist validation of our Bayesian procedure. We show that the minimax rate of contraction of the posterior…

利用高维二元空间数据校准冰盖模型AI 解读

Rapid retreat of ice in the Amundsen Sea sector of West Antarctica may cause drastic sea level rise, posing significant risks to populations in low-lying coastal regions. Calibration of computer models representing the behavior of the West Antarctic Ice Sheet is key for informative projections of future sea level rise. However, both the relevant observations and the model output are high-dimensional binary spatial data; existing computer model calibration methods are unable…

多个二元密度函数的联合估计及其在蛋白质环建模中的应用AI 解读

This article develops a method for simultaneous estimation of density functions for a collection of populations of protein backbone angle pairs using a data-driven, shared basis that is constructed by bivariate spline functions defined on a triangulation of the bivariate domain. The circular nature of angular data is taken into account by imposing appropriate smoothness constraints across boundaries of the triangles. Maximum penalized likelihood is used to fit the model and…

跨转录组研究识别疾病亚型的稀疏 K 均值元分析框架AI 解读

Disease phenotyping by omics data has become a popular approach that potentially can lead to better personalized treatment. Identifying disease subtypes via unsupervised machine learning is the first step toward this goal. In this article, we extend a sparse K-means method toward a meta-analytic framework to identify novel disease subtypes when expression profiles of multiple cohorts are available. The lasso regularization and meta-analysis identify a unique set of gene…

利用先验信息的广义线性模型变量选择：prior LASSOAI 解读

LASSO is a popular statistical tool often used in conjunction with generalized linear models that can simultaneously select variables and estimate parameters. When there are many variables of interest, as in current biological and biomedical studies, the power of LASSO can be limited. Fortunately, so much biological and biomedical data have been collected and they may contain useful information about the importance of certain variables. This paper proposes an extension of…

Lexis 图回归模型的约束估计与一致性AI 解读

This article considers a regression model on a Lexis diagram of an a × p table with a single response in each cell following a distribution in the exponential family. A regression model on the fixed effects of a rows, p columns, and a + p − 1 diagonals induces a singular design matrix and yields multiple estimators, leading to parameter identifiability problem in age–period–cohort analysis in social sciences, demography, and epidemiology, where assessment of secular trend in…

高维分类中的非参数特征增广与选择：FANSAI 解读

We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding…

高维线性回归中的样条 LassoAI 解读

We consider a high-dimensional linear regression problem, where the covariates (features) are ordered in some meaningful way, and the number of covariates p can be much larger than the sample size n. The fused lasso of Tibshirani et al. is designed especially to tackle this type of problems; it yields sparse coefficients and selects grouped variables, and encourages local constant coefficient profile within each group. However, in some applications, the effects of different…

相关变量高维模型中的层级检验AI 解读

We propose a method for testing whether hierarchically ordered groups of potentially correlated variables are significant for explaining a response in a high-dimensional linear model. In presence of highly correlated variables, as is very common in high-dimensional data, it seems indispensable to go beyond an approach of inferring individual regression coefficients, and we show that detecting smallest groups of variables (MTDs: minimal true detections) is realistic. Thanks…

潜在因子模型中的个性化预测与稀疏性追求AI 解读

Yunzhang Zhu, Xiaotong Shen & Changqing YeYunzhang Zhu (E-mail: zhuxx351@umn.edu), Xiaotong Shen (E-mail: shenx002@umn.edu), and Changqing Ye (E-mail: cqye@stat.umn.edu), School of Statistics, University of Minnesota, Minneapolis, MN 55455. Research supported in part by NSF grants DMS-1207771 and DMS-1415500, NIH grants R02GM08153 and R01HL105397. The authors would like to thank Professor Hui Jiang for technical help in OpenMP coding, and thank the editor, the associate…

格点图观测随机变量的协方差算子极小极大与自适应估计AI 解读

Covariance structure plays an important role in high-dimensional statistical inference. In a range of applications including imaging analysis and fMRI studies, random variables are observed on a lattice graph. In such a setting, it is important to account for the lattice structure when estimating the covariance operator. In this article, we consider both minimax and adaptive estimation of the covariance operator over collections of polynomially decaying and exponentially…

部分工具变量无效时的工具变量估计及孟德尔随机化应用AI 解读

Instrumental variables have been widely used for estimating the causal effect between exposure and outcome. Conventional estimation methods require complete knowledge about all the instruments’ validity; a valid instrument must not have a direct effect on the outcome and not be related to unmeasured confounders. Often, this is impractical as highlighted by Mendelian randomization studies where genetic markers are used as instruments and complete knowledge about instruments’…

空间尾部依赖的 M 估计量AI 解读

Summary Tail dependence models for distributions attracted to a max-stable law are fitted by using observations above a high threshold. To cope with spatial, high dimensional data, a rank-based M-estimator is proposed relying on bivariate margins only. A data-driven weight matrix is used to minimize the asymptotic variance. Empirical process arguments show that the estimator is consistent and asymptotically normal. Its finite sample performance is assessed in simulation…

Lasso 回归：通过 Gibbs 抽样的极限实现估计与收缩AI 解读

Summary The application of the lasso is espoused in high dimensional settings where only a small number of the regression coefficients are believed to be non-zero (i.e. the solution is sparse). Moreover, statistical properties of high dimensional lasso estimators are often proved under the assumption that the correlation between the predictors is bounded. In this vein, co-ordinatewise methods, which are the most common means of computing the lasso solution, naturally work…

可能存在变点的高维回归中的 LassoAI 解读

Summary We consider a high dimensional regression model with a possible change point due to a covariate threshold and develop the lasso estimator of regression coefficients as well as the threshold parameter. Our lasso estimator not only selects covariates but also selects a model between linear and threshold regression models. Under a sparsity assumption, we derive non-asymptotic oracle inequalities for both the prediction risk and the l1-estimation loss for regression…