A model selection method based on the adaptive LASSO-penalized GEE and weighted Gaussian pseudo-likelihood BIC in longitudinal robust analysis

In this article, a new robust variable selection approach is introduced by combining the robust generalized estimating equations and adaptive LASSO penalty function for longitudinal generalized linear models. Then, an efficient weighted Gaussian pseudo-likelihood version of the BIC (WGBIC) is proposed to choose the tuning parameter in the process of robust variable selection and to select the best working correlation structure simultaneously. Meanwhile, the oracle properties of the proposed robust variable selection method are established and an efficient algorithm combining the iterative weighted least squares and minorization–maximization is proposed to implement robust variable selection and parameter estimation.     

Variable selection in partially linear additive models for modal regression

Based on B-spline basis functions and smoothly clipped absolute deviation (SCAD) penalty, we present a new estimation and variable selection procedure based on modal regression for partially linear additive models. The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions and performs no worse than the least-square-based estimation for normal error case. The main difference is that the standard quadratic loss is replaced by a kernel function depending on a bandwidth that can be automatically selected based on the observed data. With appropriate selection of the regularization parameters, the new method possesses the consistency in variable selection and oracle property in estimation. Finally, both simulation study and real data analysis are performed to examine the performance of our approach.     

Marginalized lasso in sparse regression

We propose marginalized lasso, a new nonconvex penalization for variable selection in regression problem. The marginalized lasso penalty is motivated from integrating out the penalty parameter in the original lasso penalty with a gamma prior distribution. This study provides a thresholding rule and a lasso-based iterative algorithm for parameter estimation in the marginalized lasso. We also provide a coordinate descent algorithm to efficiently optimize the marginalized lasso penalized regression. Numerical comparison studies are provided to demonstrate its competitiveness over the existing sparsity-inducing penalizations and suggest some guideline for tuning parameter selection.     

Bayesian Elastic Net Tobit Quantile Regression

In this article, the problem of parameter estimation and variable selection in the Tobit quantile regression model is considered. A Tobit quantile regression with the elastic net penalty from a Bayesian perspective is proposed. Independent gamma priors are put on the l₁ norm penalty parameters. A novel aspect of the Bayesian elastic net Tobit quantile regression is to treat the hyperparameters of the gamma priors as unknowns and let the data estimate them along with other parameters. A Bayesian Tobit quantile regression with the adaptive elastic net penalty is also proposed. The Gibbs sampling computational technique is adapted to simulate the parameters from the posterior distributions. The proposed methods are demonstrated by both simulated and real data examples.     

Simultaneous variable and factor selection via sparse group lasso in factor analysis

This paper considers variable and factor selection in factor analysis. We treat the factor loadings for each observable variable as a group, and introduce a weighted sparse group lasso penalty to the complete log-likelihood. The proposal simultaneously selects observable variables and latent factors of a factor analysis model in a data-driven fashion; it produces a more flexible and sparse factor loading structure than existing methods. For parameter estimation, we derive an expectation-maximization algorithm that optimizes the penalized log-likelihood. The tuning parameters of the procedure are selected by a likelihood cross-validation criterion that yields satisfactory results in various simulation settings. Simulation results reveal that the proposed method can better identify the possibly sparse structure of the true factor loading matrix with higher estimation accuracy than existing methods. A real data example is also presented to demonstrate its performance in practice.     

SCAD惩罚逻辑回归的财务预警模型

作为一种有监督学习算法,逻辑回归(Logistic Regression,LR)已广泛应用于财务危机建模分析,但其潜在地存在过拟合问题。鉴此,提出一种基于平滑削边绝对偏离(Smoothly Clipped Absolute Deviation,SCAD)惩罚逻辑回归的财务预警模型。该模型不仅能很好地解决模型过拟合问题,而且还可以同时实现变量选择和模型系数估计,并提高了模型的解释性。结合沪深股市A股制造业上市公司的财务数据进行实证研究,同时对比一般的L1正则化和L2正则化逻辑回归模型的预警效果进行实证分析,实验结果表明:SCAD惩罚逻辑回归模型具有较好的分类效果和较强的经济解释能力。     

Variable selection for semiparametric varying coefficient partially linear model based on modal regression with missing data

Abstract

In this article, we focus on the variable selection for semiparametric varying coefficient partially linear model with response missing at random. Variable selection is proposed based on modal regression, where the non parametric functions are approximated by B-spline basis. The proposed procedure uses SCAD penalty to realize variable selection of parametric and nonparametric components simultaneously. Furthermore, we establish the consistency, the sparse property and asymptotic normality of the resulting estimators. The penalty estimation parameters value of the proposed method is calculated by EM algorithm. Simulation studies are carried out to assess the finite sample performance of the proposed variable selection procedure.     

Robust variable selection in modal varying-coefficient models with longitudinal

In this article we present a robust and efficient variable selection procedure by using modal regression for varying-coefficient models with longitudinal data. The new method is proposed based on basis function approximations and a group version of the adaptive LASSO penalty, which can select significant variables and estimate the non-zero smooth coefficient functions simultaneously. Under suitable conditions, we establish the consistency in variable selection and the oracle property in estimation. A simulation study and two real data examples are undertaken to assess the finite sample performance of the proposed variable selection procedure.     

Tuning Parameter Selection in Cox Proportional Hazards Model with a Diverging Number of Parameters

Regularized variable selection is a powerful tool for identifying the true regression model from a large number of candidates by applying penalties to the objective functions. The penalty functions typically involve a tuning parameter that controls the complexity of the selected model. The ability of the regularized variable selection methods to identify the true model critically depends on the correct choice of the tuning parameter. In this study, we develop a consistent tuning parameter selection method for regularized Cox's proportional hazards model with a diverging number of parameters. The tuning parameter is selected by minimizing the generalized information criterion. We prove that, for any penalty that possesses the oracle property, the proposed tuning parameter selection method identifies the true model with probability approaching one as sample size increases. Its finite sample performance is evaluated by simulations. Its practical use is demonstrated in The Cancer Genome Atlas breast cancer data.     

Regularisation Parameter Selection Via Bootstrapping

Penalised likelihood methods, such as the least absolute shrinkage and selection operator (Lasso) and the smoothly clipped absolute deviation penalty, have become widely used for variable selection in recent years. These methods impose penalties on regression coefficients to shrink a subset of them towards zero to achieve parameter estimation and model selection simultaneously. The amount of shrinkage is controlled by the regularisation parameter. Popular approaches for choosing the regularisation parameter include cross‐validation, various information criteria and bootstrapping methods that are based on mean square error. In this paper, a new data‐driven method for choosing the regularisation parameter is proposed and the consistency of the method is established. It holds not only for the usual fixed‐dimensional case but also for the divergent setting. Simulation results show that the new method outperforms other popular approaches. An application of the proposed method to motif discovery in gene expression analysis is included in this paper.     

Robust group-Lasso for functional regression model

In this article, we consider the problem of selecting functional variables using the L1 regularization in a functional linear regression model with a scalar response and functional predictors, in the presence of outliers. Since the LASSO is a special case of the penalized least-square regression with L1 penalty function, it suffers from the heavy-tailed errors and/or outliers in data. Recently, Least Absolute Deviation (LAD) and the LASSO methods have been combined (the LAD-LASSO regression method) to carry out robust parameter estimation and variable selection simultaneously for a multiple linear regression model. However, variable selection of the functional predictors based on LASSO fails since multiple parameters exist for a functional predictor. Therefore, group LASSO is used for selecting functional predictors since group LASSO selects grouped variables rather than individual variables. In this study, we propose a robust functional predictor selection method, the LAD-group LASSO, for a functional linear regression model with a scalar response and functional predictors. We illustrate the performance of the LAD-group LASSO on both simulated and real data.     

Non-iterative Estimation and Variable Selection in the Single-index Quantile Regression Model

A new estimation procedure is proposed for the single-index quantile regression model. Compared to existing work, this approach is non-iterative and hence, computationally efficient. The proposed method not only estimates the index parameter and the link function but also selects variables simultaneously. The performance of the variable selection is enhanced by a fully adaptive penalty function motivated by the sliced inverse regression technique. Finite sample performance is studied through a simulation study that compares the proposed method with existing work under several criteria. A data analysis is given that highlights the usefulness of the proposed methodology.     

面板数据的自适应Lasso分位回归方法研究

如何在对参数进行估计的同时自动选择重要解释变量,一直是面板数据分位回归模型中讨论的热点问题之一。通过构造一种含多重随机效应的贝叶斯分层分位回归模型,在假定固定效应系数先验服从一种新的条件Laplace分布的基础上,给出了模型参数估计的Gibbs抽样算法。考虑到不同重要程度的解释变量权重系数压缩程度应该不同,所构造的先验信息具有自适应性的特点,能够准确地对模型中重要解释变量进行自动选取,且设计的切片Gibbs抽样算法能够快速有效地解决模型中各个参数的后验均值估计问题。模拟结果显示,新方法在参数估计精确度和变量选择准确度上均优于现有文献的常用方法。通过对中国各地区多个宏观经济指标的面板数据进行建模分析,演示了新方法估计参数与挑选变量的能力。     

Lasso-type estimation for covariate-adjusted linear model

Lasso is popularly used for variable selection in recent years. In this paper, lasso-type penalty functions including lasso and adaptive lasso are employed in simultaneously variable selection and parameter estimation for covariate-adjusted linear model, where the predictors and response cannot be observed directly and distorted by some observable covariate through some unknown multiplicative smooth functions. Estimation procedures are proposed and some asymptotic properties are obtained under some mild conditions. It deserves noting that under appropriate conditions, the adaptive lasso estimator correctly select covariates with nonzero coefficients with probability converging to one and that the estimators of nonzero coefficients have the same asymptotic distribution that they would have if the zero coefficients were known in advance, i.e. the adaptive lasso estimator has the oracle property in the sense of Fan and Li [6]. Simulation studies are carried out to examine its performance in finite sample situations and the Boston Housing data is analyzed for illustration.     

Constrained monotone EM algorithms for mixtures of multivariate <Emphasis Type="Italic">t</Emphasis> distributions

Mixtures of multivariate t distributions provide a robust parametric extension to the fitting of data with respect to normal mixtures. In presence of some noise component, potential outliers or data with longer-than-normal tails, one way to broaden the model can be provided by considering t distributions. In this framework, the degrees of freedom can act as a robustness parameter, tuning the heaviness of the tails, and downweighting the effect of the outliers on the parameters estimation. The aim of this paper is to extend to mixtures of multivariate elliptical distributions some theoretical results about the likelihood maximization on constrained parameter spaces. Further, a constrained monotone algorithm implementing maximum likelihood mixture decomposition of multivariate t distributions is proposed, to achieve improved convergence capabilities and robustness. Monte Carlo numerical simulations and a real data study illustrate the better performance of the algorithm, comparing it to earlier proposals.     

Estimation and variable selection for generalised partially linear single-index models

In this paper, we study the problem of estimation and variable selection for generalised partially linear single-index models based on quasi-likelihood, extending existing studies on variable selection for partially linear single-index models to binary and count responses. To take into account the unit norm constraint of the index parameter, we use the ‘delete-one-component’ approach. The asymptotic normality of the estimates is demonstrated. Furthermore, the smoothly clipped absolute deviation penalty is added for variable selection of parameters both in the nonparametric part and the parametric part, and the oracle property of the variable selection procedure is shown. Finally, some simulation studies are carried out to illustrate the finite sample performance.     

Variable selection in spatial regression via penalized least squares

We consider variable selection in linear regression of geostatistical data that arise often in environmental and ecological studies. A penalized least squares procedure is studied for simultaneous variable selection and parameter estimation. Various penalty functions are considered including smoothly clipped absolute deviation. Asymptotic properties of penalized least squares estimates, particularly the oracle properties, are established, under suitable regularity conditions imposed on a random field model for the error process. Moreover, computationally feasible algorithms are proposed for estimating regression coefficients and their standard errors. Finite‐sample properties of the proposed methods are investigated in a simulation study and comparison is made among different penalty functions. The methods are illustrated by an ecological dataset of landcover in Wisconsin. The Canadian Journal of Statistics 37: 607–624; 2009 © 2009 Statistical Society of Canada     

正则化Beta回归及其应用

随着计算机的飞速发展,极大地便利了数据的获取和存储,很多企业积累了大量的数据,同时数据的维度也越来越高,噪声变量越来越多,因此在建模分析时面临的重要问题之一就是从高维的变量中筛选出少数的重要变量。针对因变量取值为(0,1)区间的比例数据提出了正则化Beta回归,研究了在LASSO、SCAD和MCP三种惩罚方法下的极大似然估计及其渐进性质。统计模拟表明MCP的方法会优于SCAD和LASSO,并且随着样本量的增大,SCAD的方法也将优于LASSO。最后,将该方法应用到中国上市公司股息率的影响因素研究中。     

Variable selection via penalized minimum φ-divergence estimation in logistic regression

We propose penalized minimum φ-divergence estimator for parameter estimation and variable selection in logistic regression. Using an appropriate penalty function, we show that penalized φ-divergence estimator has oracle property. With probability tending to 1, penalized φ-divergence estimator identifies the true model and estimates nonzero coefficients as efficiently as if the sparsity of the true model was known in advance. The advantage of penalized φ-divergence estimator is that it produces estimates of nonzero parameters efficiently than penalized maximum likelihood estimator when sample size is small and is equivalent to it for large one. Numerical simulations confirm our findings.     

Variable Selection in Joint Location and Scale Models of the Skew-t-Normal Distribution

Variable selection is an important issue in all regression analysis, and in this article, we investigate the simultaneous variable selection in joint location and scale models of the skew-t-normal distribution when the dataset under consideration involves heavy tail and asymmetric outcomes. We propose a unified penalized likelihood method which can simultaneously select significant variables in the location and scale models. Furthermore, the proposed variable selection method can simultaneously perform parameter estimation and variable selection in the location and scale models. With appropriate selection of the tuning parameters, we establish the consistency and the oracle property of the regularized estimators. These estimators are compared by simulation studies.