Regularization and variable selection via the elastic net

Summary.  We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where strongly correlated predictors tend to be in or out of the model together. The elastic net is particularly useful when the number of predictors ( p ) is much bigger than the number of observations ( n ). By contrast, the lasso is not a very satisfactory variable selection method in the p ≫ n case. An algorithm called LARS-EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lasso.     

Modern variable selection for longitudinal semi-parametric models with missing data

Penalized methods for variable selection such as the Smoothly Clipped Absolute Deviation penalty have been increasingly applied to aid variable section in regression analysis. Much of the literature has focused on parametric models, while a few recent studies have shifted the focus and developed their applications for the popular semi-parametric, or distribution-free, generalized estimating equations (GEEs) and weighted GEE (WGEE). However, although the WGEE is composed of one main and one missing-data module, available methods only focus on the main module, with no variable selection for the missing-data module. In this paper, we develop a new approach to further extend the existing methods to enable variable selection for both modules. The approach is illustrated by both real and simulated study data.     

Adaptive LASSO for varying-coefficient partially linear measurement error models

This paper extends the adaptive LASSO (ALASSO) for simultaneous parameter estimation and variable selection to a varying-coefficient partially linear model where some of the covariates are subject to measurement errors of an additive form. We draw comparisons with the SCAD, and prove that both the ALASSO and the SCAD attain the oracle property under this setup. We further develop an algorithm in the spirit of LARS for finding the solution path of the ALASSO in practical applications. Finite sample properties of the proposed methods are examined in a simulation study, and a real data example based on the U.S. Department of Agriculture's Continuing Survey of Food Intakes by Individuals (CSFII) is considered.     

Model-free variable selection

Summary.  The importance of variable selection in regression has grown in recent years as computing power has encouraged the modelling of data sets of ever-increasing size. Data mining applications in finance, marketing and bioinformatics are obvious examples. A limitation of nearly all existing variable selection methods is the need to specify the correct model before selection. When the number of predictors is large, model formulation and validation can be difficult or even infeasible. On the basis of the theory of sufficient dimension reduction, we propose a new class of model-free variable selection approaches. The methods proposed assume no model of any form, require no nonparametric smoothing and allow for general predictor effects. The efficacy of the methods proposed is demonstrated via simulation, and an empirical example is given.     

A three-stage variable selection method for supersaturated designs

A supersaturated design (SSD) is a design whose run size is not enough for estimating all main effects. Such a design is commonly used in screening experiments to screen active effects based on the effect sparsity principle. Traditional approaches, such as the ordinary stepwise regression and the best subset variable selection, may not be appropriate in this situation. In this article, a new variable selection method is proposed based on the idea of staged dimensionality reduction. Simulations and several real data studies indicate that the newly proposed method is more effective than the existing data analysis methods.     

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。     

Sure explained variability and independence screening

In the era of Big Data, extracting the most important exploratory variables available in ultrahigh-dimensional data plays a key role in scientific researches. Existing researches have been mainly focusing on applying the extracted exploratory variables to describe the central tendency of their related response variables. For a response variable, its variability characteristic is as much important as the central tendency in statistical inference. This paper focuses on the variability and proposes a new model-free feature screening approach: sure explained variability and independence screening (SEVIS). The core of SEVIS is to take the advantage of recently proposed asymmetric and nonlinear generalised measures of correlation in the screening. Under some mild conditions, the paper shows that SEVIS not only possesses desired sure screening property and ranking consistency property, but also is a computational convenient variable selection method to deal with ultrahigh-dimensional data sets with more features than observations. The superior performance of SEVIS, compared with existing model-free methods, is illustrated in extensive simulations. A real example in ultrahigh-dimensional variable selection demonstrates that the variables selected by SEVIS better explain not only the response variables, but also the variables selected by other methods.     

Nonlinear mixed-effects scalar-on-function models and variable selection

This paper is motivated by our collaborative research and the aim is to model clinical assessments of upper limb function after stroke using 3D-position and 4D-orientation movement data. We present a new nonlinear mixed-effects scalar-on-function regression model with a Gaussian process prior focusing on the variable selection from a large number of candidates including both scalar and function variables. A novel variable selection algorithm has been developed, namely functional least angle regression. As it is essential for this algorithm, we studied the representation of functional variables with different methods and the correlation between a scalar and a group of mixed scalar and functional variables. We also propose a new stopping rule for practical use. This algorithm is efficient and accurate for both variable selection and parameter estimation even when the number of functional variables is very large and the variables are correlated. And thus the prediction provided by the algorithm is accurate. Our comprehensive simulation study showed that the method is superior to other existing variable selection methods. When the algorithm was applied to the analysis of the movement data, the use of the nonlinear random-effect model and the function variables significantly improved the prediction accuracy for the clinical assessment.

     

多源高维数据的多分类纵向整合分析及应用

多分类数据分析在实证研究中具有重要意义。然而,由于高维数、小样本及低信噪比等原因,现有的多分类方法仍面临信息量不足而导致的效果不佳问题。为此,学者们通过收集更多信息源 数据以更全面地刻画实际问题。不同于收集相同自变量的不同源样本,目前较为流行的多源数据收集了相同样本的不同源自变量,它们的独立性和相关性为统计建模带来了新的挑战。本文提出基于典型变量回归的多分类纵向整合分析方法,其中利用惩罚技术实现变量选择,并独特地考虑不同源数据间的关联结构,提出高效的ADMM算法进行模型优化。数值模拟结果表明,该方法在变量选择和分类预测 上均具有优越性。基于我国上证50的多源股票数据,利用该方法对2019年股票日收益率的影响因素进行了实证探究。研究表明,本文提出的多分类整合分析在筛选出具有解释意义变量的同时具有更好的预测效果。     

A unified view on skewed distributions arising from selections

Parametric families of multivariate nonnormal distributions have received considerable attention in the past few decades. The authors propose a new definition of a selection distribution that encompasses many existing families of multivariate skewed distributions. Their work is motivated by examples that involve various forms of selection mechanisms and lead to skewed distributions. They give the main properties of selection distributions and show how various families of multivariate skewed distributions, such as the skew‐normal and skew‐elliptical distributions, arise as special cases. The authors further introduce several methods of constructing selection distributions based on linear and nonlinear selection mechanisms.     

Focused and Model Average Estimation for Regression Analysis of Panel Count Data

Panel count data arise in many fields and a number of estimation procedures have been developed along with two procedures for variable selection. In this paper, we discuss model selection and parameter estimation together. For the former, a focused information criterion (FIC) is presented and for the latter, a frequentist model average (FMA) estimation procedure is developed. A main advantage, also the difference from the existing model selection methods, of the FIC is that it emphasizes the accuracy of the estimation of the parameters of interest, rather than all parameters. Further efficiency gain can be achieved by the FMA estimation procedure as unlike existing methods, it takes into account the variability in the stage of model selection. Asymptotic properties of the proposed estimators are established, and a simulation study conducted suggests that the proposed methods work well for practical situations. An illustrative example is also provided. © 2014 Board of the Foundation of the Scandinavian Journal of Statistics     

Bayesian variable selection in a class of mixture models for ordinal data: a comparative study

In this paper, we consider a special finite mixture model named Combination of Uniform and shifted Binomial (CUB), recently introduced in the statistical literature to analyse ordinal data expressing the preferences of raters with regards to items or services. Our aim is to develop a variable selection procedure for this model using a Bayesian approach. Bayesian methods for variable selection and model choice have become increasingly popular in recent years, due to advances in Markov chain Monte Carlo computational algorithms. Several methods have been proposed in the case of linear and generalized linear models (GLM). In this paper, we adapt to the CUB model some of these algorithms: the Kuo–Mallick method together with its ‘metropolized’ version and the Stochastic Search Variable Selection method. Several simulated examples are used to illustrate the algorithms and to compare their performance. Finally, an application to real data is introduced.     

Simultaneous structure estimation and variable selection in partial linear varying coefficient models for longitudinal data

Partial linear varying coefficient models (PLVCM) are often considered for analysing longitudinal data for a good balance between flexibility and parsimony. The existing estimation and variable selection methods for this model are mainly built upon which subset of variables have linear or varying effect on the response is known in advance, or say, model structure is determined. However, in application, this is unreasonable. In this work, we propose a simultaneous structure estimation and variable selection method, which can do simultaneous coefficient estimation and three types of selections: varying and constant effects selection, relevant variable selection. It can be easily implemented in one step by employing a penalized M-type regression, which uses a general loss function to treat mean, median, quantile and robust mean regressions in a unified framework. Consistency in the three types of selections and oracle property in estimation are established as well. Simulation studies and real data analysis also confirm our method.     

Variable selection in finite mixture of semi-parametric regression models

Abstract

In this paper we are concerned with variable selection in finite mixture of semiparametric regression models. This task consists of model selection for non parametric component and variable selection for parametric part. Thus, we encountered separate model selections for every non parametric component of each sub model. To overcome this computational burden, we introduced a class of variable selection procedures for finite mixture of semiparametric regression models using penalized approach for variable selection. It is shown that the new method is consistent for variable selection. Simulations show that the performance of proposed method is good, and it consequently improves pervious works in this area and also requires much less computing power than existing methods.     

Calibrated estimators in two-stage sampling

We consider the problem of the estimation of the population mean of a study variable by assuming that the population means of an auxiliary variable are known at both stages of sample selection. The design weights at the first and second stages of sample selection are calibrated by optimizing the chi-squared type distance between the design weights and the new weights at both the first and second stages of sample selection. The regression type estimator in two-stage sampling is shown to be a special case. An application of the proposed estimators using a real data set is discussed.     

Independent feature screening for ultrahigh-dimensional models with interactions

Feature selection is an important technique for ultrahigh-dimensional data analysis. Most feature selection methods such as SIS and its relevant versions heavily depend on the specified model structures. Furthermore, feature interactions are usually not taken into account in the existing literature. In this paper, we present a novel feature selection method for the model with variable interactions, without the use of structure assumption. Thus, the new ranking criterion is flexible and can deal with the models that contain interactions. Moreover, the new screening procedures are not complex, consequently, they are computationally efficient and the theoretical properties such as the ranking consistency and sure screening properties can be easily obtained. Several real and simulation examples are presented to illustrate the methodology.     

The Loss Rank Criterion for Variable Selection in Linear Regression Analysis

Abstract. Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model selection criterion is proposed to select the best one among this preselected set. The approach leads to a fast and efficient procedure for variable selection, especially in high‐dimensional settings. Model selection consistency of the suggested criterion is proven when the number of covariates d is fixed. Simulation studies suggest that the criterion still enjoys model selection consistency when d is much larger than the sample size. The simulations also show that our approach for variable selection works surprisingly well in comparison with existing competitors. The method is also applied to a real data set.     

Detecting the Dimensionality for Principal Components Model

A crucial issue for principal components analysis (PCA) is to determine the number of principal components to capture the variability of usually high-dimensional data. In this article the dimension detection for PCA is formulated as a variable selection problem for regressions. The adaptive LASSO is used for the variable selection in this application. Simulations demonstrate that this approach is more accurate than existing methods in some cases and competitive in some others. The performance of this model is also illustrated using a real example.     

Derivative estimation and testing in generalized additive models

Estimation and testing procedures for generalized additive (interaction) models are developed. We present extensions of several existing procedures for additive models when the link is the identity. This set of methods includes estimation of all component functions and their derivatives, testing functional forms and in particular variable selection. Theorems and simulation results are presented for the fundamentally new procedures. These comprise of, in particular, the introduction of local polynomial smoothing for this kind of models and the testing, including variable selection. Our method is straightforward to implement and the simulation studies show good performance in even small data sets.