Penalized Composite Quasi-Likelihood for Ultrahigh-Dimensional Variable Selection
Reads0
Chats0
TLDR
A data‐driven weighted linear combination of convex loss functions, together with weighted L1‐penalty is proposed and established a strong oracle property of the method proposed that has both the model selection consistency and estimation efficiency for the true non‐zero coefficients.Abstract:
In high-dimensional model selection problems, penalized least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a data-driven weighted linear combination of convex loss functions, together with weighted L1-penalty. It is completely data-adaptive and does not require prior knowledge of the error distribution. The weighted L1-penalty is used both to ensure the convexity of the penalty term and to ameliorate the bias caused by the L1-penalty. In the setting with dimensionality much larger than the sample size, we establish a strong oracle property of the proposed method that possesses both the model selection consistency and estimation efficiency for the true non-zero coefficients. As specific examples, we introduce a robust method of composite L1-L2, and optimal composite quantile method and evaluate their performance in both simulated and real data examples.read more
Citations
More filters
Journal ArticleDOI
Empirical likelihood test for high dimensional linear models
TL;DR: In this article, an empirical likelihood method is proposed to test whether the coefficients in a possibly high-dimensional linear model are equal to given values, and the asymptotic distribution of the test statistic is independent of the number of covariates in the linear model.
Journal ArticleDOI
Focused vector information criterion model selection and model averaging regression with missing response
Zhimeng Sun,Zhi Su,Jingyi Ma +2 more
TL;DR: Based on the focused information criterion of Hjort and Claeskens (J Am Stat Assoc 98:879-945, 2003) and imputation idea, a frequentist model averaging estimator for a focused vector of a linear model is proposed, and the estimator is shown to be root-n consistent and asymptotical normal as mentioned in this paper.
Dissertation
Statistical Methods on Survival Data with Measurement Error
TL;DR: This thesis addresses the issue of checking the Cox model assumptions with measurement error, and proposes valid goodness of fit tests for survival data with covariate measurement error.
Posted Content
Estimation for bivariate quantile varying coefficient model
TL;DR: In this paper, a bivariate quantile regression method for the bivariate varying coefficient model through a directional approach is proposed, where the varying coefficients are approximated by the B-spline basis and an $L 2 -type penalty is imposed to achieve desired smoothness.
Journal ArticleDOI
Weighted composite quantile regression estimation and variable selection for varying coefficient models with heteroscedasticity
Hu Yang,Jing Lv,Chaohui Guo +2 more
TL;DR: In this paper, a data-driven penalized weighted composite quantile regression estimation for varying coefficient models with heteroscedasticity is proposed, which results in sparse and robust estimators simultaneously.
References
More filters
Journal ArticleDOI
Regression Shrinkage and Selection via the Lasso
TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
Journal ArticleDOI
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Jianqing Fan,Runze Li +1 more
TL;DR: In this article, penalized likelihood approaches are proposed to handle variable selection problems, and it is shown that the newly proposed estimators perform as well as the oracle procedure in variable selection; namely, they work as well if the correct submodel were known.
Journal ArticleDOI
Least angle regression
Bradley Efron,Trevor Hastie,Iain M. Johnstone,Robert Tibshirani,Hemant Ishwaran,Keith Knight,Jean-Michel Loubes,Jean-Michel Loubes,Pascal Massart,Pascal Massart,David Madigan,David Madigan,Greg Ridgeway,Greg Ridgeway,Saharon Rosset,Saharon Rosset,Ji Zhu,Robert A. Stine,Berwin A. Turlach,Sanford Weisberg +19 more
TL;DR: A publicly available algorithm that requires only the same order of magnitude of computational effort as ordinary least squares applied to the full set of covariates is described.
Journal ArticleDOI
The adaptive lasso and its oracle properties
TL;DR: A new version of the lasso is proposed, called the adaptive lasso, where adaptive weights are used for penalizing different coefficients in the ℓ1 penalty, and the nonnegative garotte is shown to be consistent for variable selection.
Journal ArticleDOI
Robust Estimation of a Location Parameter
TL;DR: In this article, a new approach toward a theory of robust estimation is presented, which treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators that are asyptotically most robust (in a sense to be specified) among all translation invariant estimators.