An elastic-net penalized expectile regression with applications

To perform variable selection in expectile regression, we introduce the elastic-net penalty into expectile regression and propose an elastic-net penalized expectile regression (ER-EN) model. We then adopt the semismooth Newton coordinate descent (SNCD) algorithm to solve the proposed ER-EN model in high-dimensional settings. The advantages of ER-EN model are illustrated via extensive Monte Carlo simulations. The numerical results show that the ER-EN model outperforms the elastic-net penalized least squares regression (LSR-EN), the elastic-net penalized Huber regression (HR-EN), the elastic-net penalized quantile regression (QR-EN) and conventional expectile regression (ER) in terms of variable selection and predictive ability, especially for asymmetric distributions. We also apply the ER-EN model to two real-world applications: relative location of CT slices on the axial axis and metabolism of tacrolimus (Tac) drug. Empirical results also demonstrate the superiority of the ER-EN model.     

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.     

语言磨蚀新问题 ——回归假说质疑

雅克布逊回归假说是语言磨蚀领域中传统的假说,随着语言磨蚀研究进一步深化,相当多的学者认可了该假说.然而,比较失语症幼儿的语言习得和磨蚀的研究结果未能证实回归假说,对健康人群的研究同样未能证实回归假说,记忆学和心理学领域也没有理论足以支持回归假说,回归假说还有很大的验证空间,它也可能并不符合语言磨蚀规律.     

Improved two-parameter estimators for the negative binomial and Poisson regression models

Negative binomial regression (NBR) and Poisson regression (PR) applications have become very popular in the analysis of count data in recent years. However, if there is a high degree of relationship between the independent variables, the problem of multicollinearity arises in these models. We introduce new two-parameter estimators (TPEs) for the NBR and the PR models by unifying the two-parameter estimator (TPE) of Özkale and Kaç?ranlar [The restricted and unrestricted two-parameter estimators. Commun Stat Theory Methods. 2007;36:2707–2725]. These new estimators are general estimators which include maximum likelihood (ML) estimator, ridge estimator (RE), Liu estimator (LE) and contraction estimator (CE) as special cases. Furthermore, biasing parameters of these estimators are given and a Monte Carlo simulation is done to evaluate the performance of these estimators using mean square error (MSE) criterion. The benefits of the new TPEs are also illustrated in an empirical application. The results show that the new proposed TPEs for the NBR and the PR models are better than the ML estimator, the RE and the LE.     

On comparing,classifying and clustering several dependent regression models

Classifying several regression models fitted on a dataset is one of the most problems in data analysis. In other words, scientists are interested in comparing several regression models that can be used for a dataset. In this paper, an approach will be used to compare and classify several dependent regression models. Then the performance of the proposed method is investigated using simulation study and real example.     

Model selection in high-dimensional noisy data: a simulation study

In many practical applications, high-dimensional regression analyses have to take into account measurement error in the covariates. It is thus necessary to extend regularization methods, that can handle the situation where the number of covariates p largely exceed the sample size n, to the case in which covariates are also mismeasured. A variety of methods are available in this context, but many of them rely on knowledge about the measurement error and the structure of its covariance matrix. In this paper, we set the goal to compare some of these methods, focusing on situations relevant for practical applications. In particular, we will evaluate these methods in setups in which the measurement error distribution and dependence structure are not known and have to be estimated from data. Our focus is on variable selection, and the evaluation is based on extensive simulations.     

Diagnostics of multiple group influential observations for logistic regression models

In this paper, two new multiple influential observation detection methods, GCD.GSPR and mCD*, are introduced for logistic regression. The proposed diagnostic measures are compared with the generalized difference in fits (GDFFITS) and the generalized squared difference in beta (GSDFBETA), which are multiple influential diagnostics. The simulation study is conducted with one, two and five independent variable logistic regression models. The performance of the diagnostic measures is examined for a single contaminated independent variable for each model and in the case where all the independent variables are contaminated with certain contamination rates and intensity. In addition, the performance of the diagnostic measures is compared in terms of the correct identification rate and swamping rate via a frequently referred to data set in the literature.     

Finite mixture of regression models for a stratified sample

Despite the popularity and importance, there is limited work on modelling data which come from complex survey design using finite mixture models. In this work, we explored the use of finite mixture regression models when the samples were drawn using a complex survey design. In particular, we considered modelling data collected based on stratified sampling design. We developed a new design-based inference where we integrated sampling weights in the complete-data log-likelihood function. The expectation–maximisation algorithm was developed accordingly. A simulation study was conducted to compare the new methodology with the usual finite mixture of a regression model. The comparison was done using bias-variance components of mean square error. Additionally, a simulation study was conducted to assess the ability of the Bayesian information criterion to select the optimal number of components under the proposed modelling approach. The methodology was implemented on real data with good results.     

Influence diagnostics in gamma ridge regression model

In this article, we proposed some influence diagnostics for the gamma regression model (GRM) and the gamma ridge regression model (GRRM). We assess the impact of influential observations on the GRM and GRRM estimates by extending the work of Pregibon [Logistic regression diagnostics. Ann Stat. 1981;9:705–724] and Walker and Birch [Influence measures in ridge regression. Technometrics. 1988;30:221–227]. Comparison of both models is made and demonstrated with the help of a simulation study and a real data set. We report some momentous results in detecting the influential observations and their effects on the GRM and GRRM estimates.     

Assessing the market values of soccer players – a robust analysis of data from German 1. and 2. Bundesliga

The paper examines to what extent a player's market value depends on his skills. Therefore, a data set covering 28 performance measures and the market values of about 493 players from 1. and 2. German Bundesliga is analysed. Applying robust analysis techniques, we are able to robustly estimate market values of soccer players. The results show (1) that there are significantly underrated and overrated players and (2) that a player's affiliation to a certain team may contribute to his market value. We conclude that a club's reputation affects the market values of its players and that star players are in tendency overrated.