Variable selection strategies in survival models with multiple imputations

In this paper, the variable selection strategies (criteria) are thoroughly discussed and their use in various survival models is investigated. The asymptotic efficiency property, in the sense of Shibata Ann Stat 8: 147-164, 1980, of a class of variable selection strategies which includes the AIC and all criteria equivalent to it, is established for a general class of survival models, such as parametric frailty or transformation models and accelerated failure time models, under minimum conditions. Furthermore, a multiple imputations method is proposed which is found to successfully handle censored observations and constitutes a competitor to existing methods in the literature. A number of real and simulated data are used for illustrative purposes.     

Variable selection in high-dimensional double generalized linear models

In this paper we are concerned with the problems of variable selection and estimation in double generalized linear models in which both the mean and the dispersion are allowed to depend on explanatory variables. We propose a maximum penalized pseudo-likelihood method when the number of parameters diverges with the sample size. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and asymptotic properties of the resulting estimators are established. We also carry out simulation studies and a real data analysis to assess the finite sample performance of the proposed variable selection procedure, showing that the proposed variable selection method works satisfactorily.     

Variable selection for multivariate generalized linear models

Generalized linear models (GLMs) are widely studied to deal with complex response variables. For the analysis of categorical dependent variables with more than two response categories, multivariate GLMs are presented to build the relationship between this polytomous response and a set of regressors. Traditional variable selection approaches have been proposed for the multivariate GLM with a canonical link function when the number of parameters is fixed in the literature. However, in many model selection problems, the number of parameters may be large and grow with the sample size. In this paper, we present a new selection criterion to the model with a diverging number of parameters. Under suitable conditions, the criterion is shown to be model selection consistent. A simulation study and a real data analysis are conducted to support theoretical findings.     

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.     

Variable selection in heterogeneous panel data models with cross-sectional dependence

This paper studies the Bridge estimator for a high-dimensional panel data model with heterogeneous varying coefficients, where the random errors are assumed to be serially correlated and cross-sectionally dependent. We establish oracle efficiency and the asymptotic distribution of the Bridge estimator, when the number of covariates increases to infinity with the sample size in both dimensions. A BIC-type criterion is also provided for tuning parameter selection. We further generalise the marginal Bridge estimator for our model to asymptotically correctly identify the covariates with zero coefficients even when the number of covariates is greater than the sample size under a partial orthogonality condition. The finite sample performance of the proposed estimator is demonstrated by simulated data examples, and an empirical application with the US stock dataset is also provided.     

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.     

Variable selection for semiparametric regression models with iterated penalization

Semiparametric regression models with multiple covariates are commonly encountered. When there are covariates not associated with response variable, variable selection may lead to sparser models, more lucid interpretations and more accurate estimation. In this study, we adopt a sieve approach for the estimation of nonparametric covariate effects in semiparametric regression models. We adopt a two-step iterated penalization approach for variable selection. In the first step, a mixture of the Lasso and group Lasso penalties are employed to conduct the first-round variable selection and obtain the initial estimate. In the second step, a mixture of the weighted Lasso and weighted group Lasso penalties, with weights constructed using the initial estimate, are employed for variable selection. We show that the proposed iterated approach has the variable selection consistency property, even when number of unknown parameters diverges with sample size. Numerical studies, including simulation and analysis of a diabetes dataset, show satisfactory performance of the proposed approach.     

Variable selection of the quantile varying coefficient regression models

As a useful supplement to mean regression, quantile regression is a completely distribution-free approach and is more robust to heavy-tailed random errors. In this paper, a variable selection procedure for quantile varying coefficient models is proposed by combining local polynomial smoothing with adaptive group LASSO. With an appropriate selection of tuning parameters by the BIC criterion, the theoretical properties of the new procedure, including consistency in variable selection and the oracle property in estimation, are established. The finite sample performance of the newly proposed method is investigated through simulation studies and the analysis of Boston house price data. Numerical studies confirm that the newly proposed procedure (QKLASSO) has both robustness and efficiency for varying coefficient models irrespective of error distribution, which is a good alternative and necessary supplement to the KLASSO method.     

Variable selection and estimation for high-dimensional spatial autoregressive models

Spatial regression models are important tools for many scientific disciplines including economics, business, and social science. In this article, we investigate postmodel selection estimators that apply least squares estimation to the model selected by penalized estimation in high-dimensional regression models with spatial autoregressive errors. We show that by separating the model selection and estimation process, the postmodel selection estimator performs at least as well as the simultaneous variable selection and estimation method in terms of the rate of convergence. Moreover, under perfect model selection, the ℓ₂ rate of convergence is the oracle rate of $\sqrt{s/n}$, compared with the convergence rate of $\text{◂√▸}\sqrt{s\log p/n}$ in the general case. Here, n is the sample size and p, s are the model dimension and number of significant covariates, respectively. We further provide the convergence rate of the estimation error in the form of $\sup$ norm, and ideally the rate can reach as fast as $\text{◂√▸}\sqrt{\log s/n}$.     

Generalized additive models with unknown link function including variable selection

The generalized additive model is a well established and strong tool that allows modelling smooth effects of predictors on the response. However, if the link function, which is typically chosen as the canonical link, is misspecified, estimates can be biased. A procedure is proposed that simultaneously estimates the form of the link function and the unknown form of the predictor functions including selection of predictors. The procedure is based on boosting methodology, which obtains estimates by using a sequence of weak learners. It strongly dominates fitting procedures that are unable to modify a given link function if the true link function deviates from the fixed function. The performance of the procedure is shown in simulation studies and illustrated by real world examples.     

Variable selection in gamma regression models via artificial bee colony algorithm

Variable selection is an important task in regression analysis. Performance of the statistical model highly depends on the determination of the subset of predictors. There are several methods to select most relevant variables to construct a good model. However in practice, the dependent variable may have positive continuous values and not normally distributed. In such situations, gamma distribution is more suitable than normal for building a regression model. This paper introduces an heuristic approach to perform variable selection using artificial bee colony optimization for gamma regression models. We evaluated the proposed method against with classical selection methods such as backward and stepwise. Both simulation studies and real data set examples proved the accuracy of our selection procedure.     

Variable selection in quantile regression when the models have autoregressive errors

This paper considers a problem of variable selection in quantile regression with autoregressive errors. Recently, Wu and Liu (2009) investigated the oracle properties of the SCAD and adaptive-LASSO penalized quantile regressions under non identical but independent error assumption. We further relax the error assumptions so that the regression model can hold autoregressive errors, and then investigate theoretical properties for our proposed penalized quantile estimators under the relaxed assumption. Optimizing the objective function is often challenging because both quantile loss and penalty functions may be non-differentiable and/or non-concave. We adopt the concept of pseudo data by Oh et al. (2007) to implement a practical algorithm for the quantile estimate. In addition, we discuss the convergence property of the proposed algorithm. The performance of the proposed method is compared with those of the majorization-minimization algorithm (Hunter and Li, 2005) and the difference convex algorithm (Wu and Liu, 2009) through numerical and real examples.     

Variable selection in linear measurement error models via penalized score functions

We propose variable selection procedures based on penalized score functions derived for linear measurement error models. To calibrate the selection procedures, we define new tuning parameter selectors based on the scores. Large-sample properties of these new tuning parameter selectors are established for the proposed procedures. These new methods are compared in simulations and a real-data application with competing methods where one ignores measurement error or uses the Bayesian information criterion to choose the tuning parameter.     

Variable selection in finite mixture of regression models using the skew-normal distribution

Variable selection in finite mixture of regression (FMR) models is frequently used in statistical modeling. The majority of applications of variable selection in FMR models use a normal distribution for regression error. Such assumptions are unsuitable for a set of data containing a group or groups of observations with asymmetric behavior. In this paper, we introduce a variable selection procedure for FMR models using the skew-normal distribution. With appropriate choice of the tuning parameters, we establish the theoretical properties of our procedure, including consistency in variable selection and the oracle property in estimation. To estimate the parameters of the model, a modified EM algorithm for numerical computations is developed. The methodology is illustrated through numerical experiments and a real data example.     

Variable selection in joint location and scale models of the skew-normal distribution

A regression model with skew-normal errors provides a useful extension for ordinary normal regression models when the data set under consideration involves asymmetric outcomes. Variable selection is an important issue in all regression analyses, and in this paper, we investigate the simultaneously variable selection in joint location and scale models of the skew-normal distribution. 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. Simulation studies and a real example are used to illustrate the proposed methodologies.     

Variable selection via the weighted group lasso for factor analysis models

We consider the problem of selecting variables in factor analysis models. The $L_1$ regularization procedure is introduced to perform an automatic variable selection. In the factor analysis model, each variable is controlled by multiple factors when there are more than one underlying factor. We treat parameters corresponding to the multiple factors as grouped parameters, and then apply the group lasso. Furthermore, the weight of the group lasso penalty is modified to obtain appropriate estimates and improve the performance of variable selection. Crucial issues in this modeling procedure include the selection of the number of factors and a regularization parameter. Choosing these parameters can be viewed as a model selection and evaluation problem. We derive a model selection criterion for evaluating the factor analysis model via the weighted group lasso. Monte Carlo simulations are conducted to investigate the effectiveness of the proposed procedure. A real data example is also given to illustrate our procedure. The Canadian Journal of Statistics 40: 345–361; 2012 © 2012 Statistical Society of Canada