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Variable selection for varying dispersion beta regression model

JOURNAL OF APPLIED STATISTICS 2014年第1期41卷 95-108页

作者： Zhao, Weihua Zhang, Riquan Lv, Yazhao Liu, Jicai NanTong Univ Sch Sci Nantong 226007 Peoples R China E China Normal Univ Sch Finance & Stat Shanghai 200241 Peoples R China Shanxi Datong Univ Dept Math Datong 037009 Peoples R China

The beta regression models are commonly used by practitioners to model variables that assume values in the standard unit interval (0, 1). In this paper, we consider the issue of variable selection for beta regression models with varying dispersion (VBRM), in which both the mean and the dispersion depend upon predictor variables. Based on a penalized likelihood method, the consistency and the oracle property of the penalized estimators are established. Following the coordinate descent algorithm idea of generalized linear models, we develop new variable selection procedure for the VBRM, which can efficiently simultaneously estimate and select important variables in both mean model and dispersion model. Simulation studies and body fat data analysis are presented to illustrate the proposed methods.

关键词： beta regression varying dispersion variable selection coordinate descent algorithm BIC

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Penalized polygram regression

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JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2022年第4期51卷 1161-1192页

作者： Jhong, Jae-Hwan Bak, Kwan-Young Koo, Ja-Yong ChungBuk Natl Univ Dept Informat Stat Cheongju South Korea Sungshin Womens Univ Sch Math Stat & Data Sci Seoul South Korea Sungshin Womens Univ Data Sci Ctr Seoul South Korea Korea Univ Dept Stat Seoul South Korea

We consider a study on regression function estimation over a bounded domain of arbitrary shapes based on triangulation and penalization techniques. A total variation type penalty is imposed to encourage fusion of adjacent triangles, which leads to a partition of the domain consisting of disjointed polygons. The proposed method provides a piecewise linear, and continuous estimator over a data adaptive polygonal partition of the domain. We adopt a coordinate decent algorithm to handle the non-separable structure of the penalty and investigate its convergence property. Regarding the asymptotic results, we establish an oracle type inequality and convergence rate of the proposed estimator. A numerical study is carried out to illustrate the performance of this method. An R software package polygram is available.

关键词： Barycentric coordinates coordinate descent algorithm Minimaxity Polygonal partitions Triangulation

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Variable selection and estimation in generalized linear models with the seamless L₀ penalty

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CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 2012年第4期40卷 745-769页

作者： Li, Zilin Wang, Sijian Lin, Xihong Harvard Univ Dept Biostat Boston MA 02115 USA Tsinghua Univ Dept Math Beijing 100084 Peoples R China Univ Wisconsin Dept Biostat & Med Informat Madison WI USA Univ Wisconsin Dept Stat Madison WI 53706 USA

In this paper, we propose variable selection and estimation in generalized linear models using the seamless $L_0$ (SELO) penalized likelihood approach. The SELO penalty is a smooth function that very closely resembles the discontinuous $L_0$ penalty. We develop an efficient algorithm to fit the model, and show that the SELO-GLM procedure has the oracle property in the presence of a diverging number of variables. We propose a Bayesian information criterion (BIC) to select the tuning parameter. We show that under some regularity conditions, the proposed SELO-GLM/BIC procedure consistently selects the true model. We perform simulation studies to evaluate the finite sample performance of the proposed methods. Our simulation studies show that the proposed SELO-GLM procedure has a better finite sample performance than several existing methods, especially when the number of variables is large and the signals are weak. We apply the SELO-GLM to analyze a breast cancer genetic dataset to identify the SNPs that are associated with breast cancer risk. The Canadian Journal of Statistics 40: 745769;2012 (C) 2012 Statistical Society of Canada

关键词： BIC consistency coordinate descent algorithm model selection oracle property penalized likelihood methods SELO penalty tuning parameter selection

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Outlier detection under a covariate-adjusted exponential regression model with censored data

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COMPUTATIONAL STATISTICS 2021年第2期36卷 961-976页

作者： Pan, Yingli Liu, Zhan Song, Guangyu Hubei Univ Fac Math & Stat Hubei Key Lab Appl Math Wuhan 430062 Peoples R China

Exponential regression models with censored data are most widely used in practice. In the modeling process, there exist situations where the covariates are not directly observed but are observed after being contaminated by unknown functions of an observable confounder in a multiplicative manner. The problem of outlier detection is a fundamental and important problem in applied statistics. In this paper, we use a nonparametric regression method to adjust the covariates and recast the outlier detection issue into a high-dimensional regularization regression issue in the covariate-adjusted exponential regression model with censored data. We propose a smoothly clipped absolute deviation (SCAD) penalized likelihood method to detect the possible outliers, which features that the proposed method can simultaneously deal with outlier detection and estimations for the regression coefficients. The coordinate descent algorithm is employed to facilitate computation. Simulation studies are conducted to evaluate the finite-sample performance of our proposed method. An application to a German breast cancer study demonstrates the utility of the proposed method in practice.

关键词： Outlier diagnosis Contaminated covariate SCAD coordinate descent algorithm

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Variable selection approach for zero-inflated count data via adaptive lasso

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JOURNAL OF APPLIED STATISTICS 2014年第4期41卷 879-894页

作者： Zeng, Ping Wei, Yongyue Zhao, Yang Liu, Jin Liu, Liya Zhang, Ruyang Gou, Jianwei Huang, Shuiping Chen, Feng Nanjing Med Univ Dept Epidemiol & Biostat Nanjing Jiangsu Peoples R China Xuzhou Med Coll Dept Epidemiol & Biostat Xuzhou Peoples R China

This article proposes a variable selection approach for zero-inflated count data analysis based on the adaptive lasso technique. Two models including the zero-inflated Poisson and the zero-inflated negative binomial are investigated. An efficient algorithm is used to minimize the penalized log-likelihood function in an approximate manner. Both the generalized cross-validation and Bayesian information criterion procedures are employed to determine the optimal tuning parameter, and a consistent sandwich formula of standard errors for nonzero estimates is given based on local quadratic approximation. We evaluate the performance of the proposed adaptive lasso approach through extensive simulation studies, and apply it to analyze real-life data about doctor visits.

关键词： adaptive lasso variable selection zero-inflated Poisson zero-inflated negative binomial coordinate descent algorithm Taylor approximation

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Group penalized quantile regression

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STATISTICAL METHODS AND APPLICATIONS 2022年第3期31卷 495-529页

作者： Ouhourane, Mohamed Yang, Yi Benedet, Andrea L. Oualkacha, Karim Univ Quebec Dept Math Montreal PQ Canada McGill Univ Dept Math & Stat Montreal PQ Canada McGill Univ Translat Neuroimaging Lab Res Ctr Studies Aging Montreal PQ Canada

Quantile regression models have become a widely used statistical tool in genetics and in the omics fields because they can provide a rich description of the predictors' effects on an outcome without imposing stringent parametric assumptions on the outcome-predictors relationship. This work considers the problem of selecting grouped variables in high-dimensional linear quantile regression models. We introduce a group penalized pseudo quantile regression (GPQR) framework with both group-lasso and group non-convex penalties. We approximate the quantile regression check function using a pseudo-quantile check function. Then, using the majorization-minimization principle, we derive a simple and computationally efficient group-wise descent algorithm to solve group penalized quantile regression. We establish the convergence rate property of our algorithm with the group-Lasso penalty and illustrate the GPQR approach performance using simulations in high-dimensional settings. Furthermore, we demonstrate the use of the GPQR method in a gene-based association analysis of data from the Alzheimer's Disease Neuroimaging Initiative study and in an epigenetic analysis of DNA methylation data.

关键词： coordinate descent algorithm Group penalized regression Heterogeneous Pseudo-quantile Variable selection Quantile regression

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Sparse factor regression via penalized maximum likelihood estimation

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STATISTICAL PAPERS 2018年第2期59卷 633-662页

作者： Hirose, Kei Imada, Miyuki Kyushu Univ Inst Math Ind Nishi Ku 744 Motooka Fukuoka 8190395 Japan NTT Network Innovat Labs 3-9-11 Midori Cho Musashino Tokyo 1808585 Japan

In factor regression model, the maximum likelihood estimation suffers from three disadvantages: (i) the maximum likelihood estimates are unavailable when the number of variables exceeds the number of observations, (ii) the rotation technique based on maximum likelihood estimates produces an insufficiently sparse loading matrix, and (iii) multicollinearity can occur when the estimates of unique variances (specific variances) are small because the regression coefficients are sensitive to the inverse of unique variances. To handle these problems, we propose a penalized maximum likelihood procedure. Specifically, we impose a lasso-type penalty on the factor loadings to improve the sparseness of the solution. We also introduce a penalty on unique variances, which (given the factor scores) corresponds to the ridge penalty on the regression coefficient. Theoretical properties from a prediction viewpoint of our procedure are discussed. The effectiveness of the procedure is investigated through Monte Carlo simulations. The utility of our procedure is demonstrated on real data collected by an online questionnaire.

关键词： coordinate descent algorithm Lasso Multicollinearity Penalized maximum likelihood estimation Rotation technique

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Sparse estimation via nonconcave penalized likelihood in factor analysis model

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STATISTICS AND COMPUTING 2015年第5期25卷 863-875页

作者： Hirose, Kei Yamamoto, Michio Osaka Univ Grad Sch Engn Sci Div Math Sci Toyonaka Osaka 5608531 Japan Kyoto Univ Dept Biomed Stat & Bioinformat Grad Sch Med Sakyo Ku Kyoto 6068507 Japan

We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is utilized to find sparse factor loadings. However, the maximum likelihood estimates cannot be obtained when the number of variables is much larger than the number of observations. Furthermore, even if the maximum likelihood estimates are available, the rotation technique does not often produce a sufficiently sparse solution. In order to handle these problems, this paper introduces a penalized likelihood procedure that imposes a nonconvex penalty on the factor loadings. We show that the penalized likelihood procedure can be viewed as a generalization of the traditional two-step approach, and the proposed methodology can produce sparser solutions than the rotation technique. A new algorithm via the EM algorithm along with coordinate descent is introduced to compute the entire solution path, which permits the application to a wide variety of convex and nonconvex penalties. Monte Carlo simulations are conducted to investigate the performance of our modeling strategy. A real data example is also given to illustrate our procedure.

关键词： coordinate descent algorithm Factor analysis Nonconvex penalty Penalized likelihood Rotation technique

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Empirical Likelihood for Censored Linear Regression and Variable Selection

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SCANDINAVIAN JOURNAL OF STATISTICS 2015年第3期42卷 798-812页

作者： Wu, Tong Tong Li, Gang Tang, Chengyong Univ Rochester Dept Biostat & Computat Biol Rochester NY 14627 USA Univ Calif Los Angeles Dept Biostat Los Angeles CA 90024 USA Temple Univ Fox Sch Business Dept Stat Philadelphia PA 19122 USA

The linear regression model for right censored data, also known as the accelerated failure time model using the logarithm of survival time as the response variable, is a useful alternative to the Cox proportional hazards model. Empirical likelihood as a non-parametric approach has been demonstrated to have many desirable merits thanks to its robustness against model misspecification. However, the linear regression model with right censored data cannot directly benefit from the empirical likelihood for inferences mainly because of dependent elements in estimating equations of the conventional approach. In this paper, we propose an empirical likelihood approach with a new estimating equation for linear regression with right censored data. A nested coordinate algorithm with majorization is used for solving the optimization problems with non-differentiable objective function. We show that the Wilks' theorem holds for the new empirical likelihood. We also consider the variable selection problem with empirical likelihood when the number of predictors can be large. Because the new estimating equation is non-differentiable, a quadratic approximation is applied to study the asymptotic properties of penalized empirical likelihood. We prove the oracle properties and evaluate the properties with simulated data. We apply our method to a Surveillance, Epidemiology, and End Results small intestine cancer dataset.

关键词： accelerated failure time model coordinate descent algorithm high-dimensional data analysis linear regression model oracle property variable selection Wilks' theorem

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The shooting S-estimator for robust regression

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COMPUTATIONAL STATISTICS 2016年第3期31卷 829-844页

作者： Ollerer, Viktoria Alfons, Andreas Croux, Christophe Katholieke Univ Leuven Fac Econ & Business Naamsestr 69 B-3000 Louvain Belgium Erasmus Univ Erasmus Sch Econ POB 1738 NL-3000 DR Rotterdam Netherlands

To perform multiple regression, the least squares estimator is commonly used. However, this estimator is not robust to outliers. Therefore, robust methods such as S-estimation have been proposed. These estimators flag any observation with a large residual as an outlier and downweight it in the further procedure. However, a large residual may be caused by an outlier in only one single predictor variable, and downweighting the complete observation results in a loss of information. Therefore, we propose the shooting S-estimator, a regression estimator that is especially designed for situations where a large number of observations suffer from contamination in a small number of predictor variables. The shooting S-estimator combines the ideas of the coordinate descent algorithm with simple S-regression, which makes it robust against componentwise contamination, at the cost of failing the regression equivariance property.

关键词： Cellwise outliers Componentwise contamination Shooting algorithm coordinate descent algorithm Regression S-estimation

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