Outlier detection and robust variable selection via the penalized weighted LAD-LASSO method

This paper studies the outlier detection and robust variable selection problem in the linear regression model. The penalized weighted least absolute deviation (PWLAD) regression estimation method and the adaptive least absolute shrinkage and selection operator (LASSO) are combined to simultaneously achieve outlier detection, and robust variable selection. An iterative algorithm is proposed to solve the proposed optimization problem. Monte Carlo studies are evaluated the finite-sample performance of the proposed methods. The results indicate that the finite sample performance of the proposed methods performs better than that of the existing methods when there are leverage points or outliers in the response variable or explanatory variables. Finally, we apply the proposed methodology to analyze two real datasets.     

WLAD-LASSO method for robust estimation and variable selection in partially linear models

This paper focuses on robust estimation and variable selection for partially linear models. We combine the weighted least absolute deviation (WLAD) regression with the adaptive least absolute shrinkage and selection operator (LASSO) to achieve simultaneous robust estimation and variable selection for partially linear models. Compared with the LAD-LASSO method, the WLAD-LASSO method will resist to the heavy-tailed errors and outliers in the parametric components. In addition, we estimate the unknown smooth function by a robust local linear regression. Under some regular conditions, the theoretical properties of the proposed estimators are established. We further examine finite-sample performance of the proposed procedure by simulation studies and a real data example.     

A comparison of robust versions of the AIC based on M-, S- and MM-estimators

Variable selection in the presence of outliers may be performed by using a robust version of Akaike's information criterion (AIC). In this paper, explicit expressions are obtained for such criteria when S- and MM-estimators are used. The performance of these criteria is compared with the existing AIC based on M-estimators and with the classical non-robust AIC. In a simulation study and in data examples, we observe that the proposed AIC with S and MM-estimators selects more appropriate models in case outliers are present.     

The performances of several modified CIC criteria for working intra-cluster correlation structure selection in GEE analysis

Based on various improved robust covariance estimators in the literature, several modified versions of the well-known correlated information criterion (CIC) for working intra-cluster correlation structure (ICS) selection are proposed. Performances of these modified criteria are examined and compared to the CIC via simulations. When the response is Gaussian, binary, or Poisson, the modified criteria are demonstrated to have higher detection rates when the true ICS is exchangeable, while the CIC would perform better when the true ICS is AR(1). An application of the criteria is made to a real dataset.     

Structure identification and variable selection in geographically weighted regression models

Geographically weighted regression (GWR) is an important tool for exploring spatial non-stationarity of a regression relationship, in which whether a regression coefficient really varies over space is especially important in drawing valid conclusions on the spatial variation characteristics of the regression relationship. This paper proposes a so-called GWGlasso method for structure identification and variable selection in GWR models. This method penalizes the loss function of the local-linear estimation of the GWR model by the coefficients and their partial derivatives in the way of the adaptive group lasso and can simultaneously identify spatially varying coefficients, nonzero constant coefficients and zero coefficients. Simulation experiments are further conducted to assess the performance of the proposed method and the Dublin voter turnout data set is analysed to demonstrate its application.     

A systematic review on model selection in high-dimensional regression

High dimensional models are getting much attention from diverse research fields involving very many parameters with a moderate size of data. Model selection is an important issue in such a high dimensional data analysis. Recent literature on theoretical understanding of high dimensional models covers a wide range of penalized methods including LASSO and SCAD. This paper presents a systematic overview of the recent development in high dimensional statistical models. We provide a brief review on the recent development of theory, methods, and guideline on applications of several penalized methods. The review includes appropriate settings to be implemented and limitations along with potential solution for each of the reviewed method. In particular, we provide a systematic review of statistical theory of the high dimensional methods by considering a unified high-dimensional modeling framework together with high level conditions. This framework includes (generalized) linear regression and quantile regression as its special cases. We hope our review helps researchers in this field to have a better understanding of the area and provides useful information to future study.     

Joint analysis of occurrence and time to stability after entrance into the Italian labour market: an approach based on a Bayesian cure model with structured stochastic search variable selection

Precarious employment is a serious social problem, especially in those countries, such as Italy, where there are limited benefits from social security. We investigate this phenomenon by analysing the initial part of the career of employees starting with unstable contracts for a panel of Italian workers. Our aim is to estimate the probability of getting a stable job and to detect factors influencing both this probability and the duration of precariousness. To answer these questions, we use an ad hoc mixture cure rate model in a Bayesian framework.     

Consistent model selection and data-driven smooth tests for longitudinal data in the estimating equations approach

Summary.  Model selection for marginal regression analysis of longitudinal data is challenging owing to the presence of correlation and the difficulty of specifying the full likelihood, particularly for correlated categorical data. The paper introduces a novel Bayesian information criterion type model selection procedure based on the quadratic inference function, which does not require the full likelihood or quasi-likelihood. With probability approaching 1, the criterion selects the most parsimonious correct model. Although a working correlation matrix is assumed, there is no need to estimate the nuisance parameters in the working correlation matrix; moreover, the model selection procedure is robust against the misspecification of the working correlation matrix. The criterion proposed can also be used to construct a data-driven Neyman smooth test for checking the goodness of fit of a postulated model. This test is especially useful and often yields much higher power in situations where the classical directional test behaves poorly. The finite sample performance of the model selection and model checking procedures is demonstrated through Monte Carlo studies and analysis of a clinical trial data set.     

A method for checking regression models in survival analysis based on the risk score

We propose to perform model check for the Cox and Aalen regression models using martingale residual processes grouped after the risk score. Asymptotic distributions of the grouped martingale residual processes are deduced, so both formal and graphical model check can be performed. The method is validated by stochastic simulation. A data example with patients with primary biliary cirrhosis of the liver is discussed.