论文检索

预测变量数量增长且高度相关时的分布加权偏最小二乘AI 解读

Summary Because highly correlated data arise from many scientific fields, we investigate parameter estimation in a semiparametric regression model with diverging number of predictors that are highly correlated. For this, we first develop a distribution-weighted least squares estimator that can recover directions in the central subspace, then use the distribution-weighted least squares estimator as a seed vector and project it onto a Krylov space by partial least squares to…

一类半参数线性模型的平滑参数选择AI 解读

Summary Spline-based approaches to non-parametric and semiparametric regression, as well as to regression of scalar outcomes on functional predictors, entail choosing a parameter controlling the extent to which roughness of the fitted function is penalized. We demonstrate that the equations determining two popular methods for smoothing parameter selection, generalized cross-validation and restricted maximum likelihood, share a similar form that allows us to prove several…

广义惩罚样条平滑的若干渐近结果AI 解读

Summary The paper discusses asymptotic properties of penalized spline smoothing if the spline basis increases with the sample size. The proof is provided in a generalized smoothing model allowing for non-normal responses. The results are extended in two ways. First, assuming the spline coefficients to be a priori normally distributed links the smoothing framework to generalized linear mixed models. We consider the asymptotic rates such that the Laplace approximation is…

未知方差下的高斯模型选择AI 解读

Let Y be a Gaussian vector whose components are independent with a common unknown variance. We consider the problem of estimating the mean μ of Y by model selection. More precisely, we start with a collection $\mathcal{S}=\{S_{m},m\in\mathcal{M}\}$ of linear subspaces of ℝn and associate to each of these the least-squares estimator of μ on Sm. Then, we use a data driven penalized criterion in order to select one estimator among these. Our first objective is to analyze the…

高维部分线性模型中的 SCAD 惩罚回归AI 解读

We consider the problem of simultaneous variable selection and estimation in partially linear models with a divergent number of covariates in the linear part, under the assumption that the vector of regression coefficients is sparse. We apply the SCAD penalty to achieve sparsity in the linear part and use polynomial splines to estimate the nonparametric component. Under reasonable conditions, it is shown that consistency in terms of variable selection and estimation can be…

非线性固定效应面板模型中降低偏差的惩罚函数方法AI 解读

We consider estimation of nonlinear panel data models with individual specific fixed effects. Estimation of these models is complicated since estimation of the fixed effects when the time dimension is short generally results in inconsistent estimates of all model parameters. We present a penalized objective function that reduces the bias in the resulting point estimates. The penalty function is simple to construct and requires no modification for models with multiple…

带测量误差的部分线性模型变量选择AI 解读

This article focuses on variable selection for partially linear models when the covariates are measured with additive errors. We propose two classes of variable selection procedures, penalized least squares and penalized quantile regression, using the nonconvex penalized principle. The first procedure corrects the bias in the loss function caused by the measurement error by applying the so-called correction-for-attenuation approach, whereas the second procedure corrects the…

具有半参数因子动态的时间序列建模AI 解读

High-dimensional regression problems, which reveal dynamic behavior, are typically analyzed by time propagation of a few number of factors. The inference on the whole system is then based on the low-dimensional time series analysis. Such high-dimensional problems occur frequently in many different fields of science. In this article we address the problem of inference when the factors and factor loadings are estimated by semiparametric methods. This more flexible modeling…

单倍型病例对照研究中兼顾稳健性与效率的收缩估计AI 解读

Case-control association studies often aim to investigate the role of genes and gene-environment interactions in terms of the underlying haplotypes (i.e., the combinations of alleles at multiple genetic loci along chromosomal regions). The goal of this article is to develop robust but efficient approaches to the estimation of disease odds-ratio parameters associated with haplotypes and haplotype-environment interactions. We consider "shrinkage" estimation techniques that can…

大型协方差矩阵的广义阈值化AI 解读

We propose a new class of generalized thresholding operators that combine thresholding with shrinkage, and study generalized thresholding of the sample covariance matrix in high dimensions. Generalized thresholding of the covariance matrix has good theoretical properties and carries almost no computational burden. We obtain an explicit convergence rate in the operator norm that shows the tradeoff between the sparsity of the true model, dimension, and the sample size, and…

利用非光滑惩罚选择有限混合模型的阶数AI 解读

Order selection is a fundamental and challenging problem in the application of finite mixture models. In this article, we develop a new penalized likelihood approach. The new method, modified smoothly clipped absolute deviation (MSCAD), deviates from information-based methods such as Akaike information criterion (AIC) and Bayesian information criterion (BIC) by introducing two penalty functions that depend on the mixing proportions and the component parameters. It is…

高维数据稀疏表示的Lasso型恢复AI 解读

The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables pn is potentially much larger than the number of samples n. However, it was recently discovered that the sparsity pattern of the Lasso estimator can only be asymptotically identical to the true sparsity pattern if the design matrix satisfies the so-called irrepresentable condition. The latter condition can easily be violated in the…

跳跃惩罚最小二乘估计的一致性与收敛速度AI 解读

We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L2([0, 1)) our results cover other metrics like Skorokhod metric on the space of càdlàg functions and uniform metrics on C([0, 1]). We will show that these estimators are in an adaptive sense rate optimal over certain classes of “approximation spaces.”…

Lasso 型广义矩估计量AI 解读

This paper proposes the least absolute shrinkage and selection operator–type (Lasso-type) generalized method of moments (GMM) estimator. This Lasso-type estimator is formed by the GMM objective function with the addition of a penalty term. The exponent of the penalty term in the regular Lasso estimator is equal to one. However, the exponent of the penalty term in the Lasso-type estimator is less than one in the analysis here. The magnitude of the exponent is reduced to avoid…

用于无模型变量选择的收缩逆回归估计AI 解读

Summary The family of inverse regression estimators that was recently proposed by Cook and Ni has proven effective in dimension reduction by transforming the high dimensional predictor vector to its low dimensional projections. We propose a general shrinkage estimation strategy for the entire inverse regression estimation family that is capable of simultaneous dimension reduction and variable selection. We demonstrate that the new estimators achieve consistency in variable…

DASSO：Dantzig 选择器与 Lasso 的联系AI 解读

Summary We propose a new algorithm, DASSO, for fitting the entire coefficient path of the Dantzig selector with a similar computational cost to the least angle regression algorithm that is used to compute the lasso. DASSO efficiently constructs a piecewise linear path through a sequential simplex-like algorithm, which is remarkably similar to the least angle regression algorithm. Comparison of the two algorithms sheds new light on the question of how the lasso and Dantzig…

含序列相关不可观测状态变量的动态离散选择模型推断AI 解读

This paper develops a method for inference in dynamic discrete choice models with serially correlated unobserved state variables. Estimation of these models involves computing high-dimensional integrals that are present in the solution to the dynamic program and in the likelihood function. First, the paper proposes a Bayesian Markov chain Monte Carlo estimation procedure that can handle the problem of multidimensional integration in the likelihood function. Second, the paper…

大型因子模型中因子数量的假设检验AI 解读

In this paper we study high-dimensional time series that have the generalized dynamic factor structure. We develop a test of the null of k0 factors against the alternative that the number of factors is larger than k0 but no larger than k1>k0. Our test statistic equals maxk0

统计交互作用的多重稳健推断AI 解读

A primary focus of an increasing number of scientific studies is to determine whether two exposures interact in the effect that they produce on an outcome of interest. Interaction is commonly assessed by fitting regression models in which the linear predictor includes the product between those exposures. When the main interest lies in the interaction, this approach is not entirely satisfactory because it is prone to (possibly severe) bias when the main exposure effects or…

采用非光滑惩罚的有限混合模型阶数选择AI 解读

Order selection is a fundamental and challenging problem in the application of finite mixture models. We develop a new penalized likelihood approach that we call MSCAD. MSCAD deviates from information-based methods, such as Akaike information criterion and the Bayes information criterion, by introducing two penalty functions that depend on the mixing proportions and the component parameters. It is consistent in estimating both the order of the mixture model and the mixing…

高维情形下的平滑截断绝对偏差估计AI 解读

The smoothly clipped absolute deviation (SCAD) estimator, proposed by Fan and Li, has many desirable properties, including continuity, sparsity, and unbiasedness. The SCAD estimator also has the (asymptotically) oracle property when the dimension of covariates is fixed or diverges more slowly than the sample size. In this article we study the SCAD estimator in high-dimensional settings where the dimension of covariates can be much larger than the sample size. First, we…

二元结局预测中变量选择的随机优化比较及卫生政策应用AI 解读

Traditional variable-selection strategies in generalized linear models (GLMs) seek to optimize a measure of predictive accuracy without regard for the cost of data collection. When the purpose of such model building is the creation of predictive scales to be used in future studies with constrained budgets, the standard approach may not be optimal. We propose a Bayesian decision-theoretic framework for variable selection in binary-outcome GLMs where the budget for data…

非参数变量选择：EARTH算法AI 解读

We consider regression experiments involving a response variable Y and a large number of predictor variables X1, …, Xd, many of which may be irrelevant for the prediction of Y and thus must be removed before Y can be predicted from the X’s. We consider two procedures that select variables by using importance scores that measure the strength of the relationship between predictor variables and a response and keep those variables whose importance scores exceed a threshold. In…

高维稀疏因子建模：基因表达组学应用AI 解读

We describe studies in molecular profiling and biological pathway analysis that use sparse latent factor and regression models for microarray gene expression data. We discuss breast cancer applications and key aspects of the modeling and computational methodology. Our case studies aim to investigate and characterize heterogeneity of structure related to specific oncogenic pathways, as well as links between aggregate patterns in gene expression profiles and clinical…