Quantile regression for singleindexcoefficient regression. Abstract regression problems with many potential candidate predictor variables occur in a wide variety of scienti. On the ultrahigh dimensional linear discriminant analysis problem with a diverging number of classes. A full range of quantile analysis can provide more complete. In set up ii and iii, the penalized quantile regression at single quantile level tends to miss relevant variables when the target quantile level is outside of the quantile index range, where these covariates have effects. Algorithm is similar to lasso code presented in koenker and mizera 2014. Using more appropriate unconditional quantile regression models, we find, in contrast to budig and hodgess claims, that the motherhood penalty is not largest for lowwage women. Introduction since the seminal work of koenker and bassett 1978, quantile regression. Nonparametric quantile regression with multivariate covariates is a difficult estimation problem due to the curse of dimensionality. Mar 31, 2016 in this paper, a minimizing average check loss estimation macle procedure is proposed for the single index coefficient model sicm in the framework of quantile regression qr. Citeseerx published by canadian center of science and.
Is the motherhood penalty larger for lowwage women. Rubinfeld 1978 based on a linear regression analysis. However, whereas leastsquares regression is concerned with modelling the conditional mean. We propose a new algorithm for simultaneous variable selection and parameter estimation for the single index quantile regression siqr model. Estimating quantile regression models for independent. This package provides functions to find solutions to penalized quantile regression problems. This is for downstream analysis for fitting models with missing data. Regularized quantile regression and robust feature screening. By using adaptive weights for penalizing different coefficients in the lasso penalty. Singleindex quantile regression with lasso penalty lsiq the lasso is proposed by tibshirani 1996 for simultaneous variable selection and parameter estimation.
Consistent model identification of varying coefficient. As an empirical study, we apply the singleindex quantile regression model to. A variety of model selection methods are available, including forward, backward, stepwise, lasso, and leastangle regression. We proposed applying penalized quantile regression for computing. Estimation and inference methods for models of conditional quantiles. Inference for single index quantile regression models with profile optimization ma, shujie and he, xuming, the annals of statistics, 2016. Keywords earnings, family, working parents, quantitative methods, quantile regression. Thus, the precision of parameter estimation as well as the accuracy of prediction will be e. Furthermore, we propose a variable selection procedure for the qr of sim by combining the estimation method with the adaptive lasso penalized method to get sparse estimation of the index.
On assessing prior distributions and bayesian regression analysis with g. The process offers extensive capabilities for customizing the selection with a wide variety of selection and. In this paper, we propose a new full iteration estimation method for quantile regression qr of the single index model sim. Quantile regression of partial linear single index model 377 posite quantile regression cqr, proposed by zou and yuan 2008 of sim. For our singleindex quantile regression model 1, note g0. Polynomial splines are used to estimate the unknown link function. Expectile and quantile regressiondavid and goliath. Singleindex quantile regression journal of multivariate. This paper is concerned with quantile regression for single index coefficient regression models. Bayesian tobit quantile regression with singleindex. Quantile regression and variable selection of partial linear single index model.
The asymptotic properties of the proposed estimator are derived. Group penalties use the l1 norm instead of l2 for computational convenience. Semiparametric modeling and estimation of heteroscedasticity in regression. Penalized quantile regression with semiparametric correlated effects. A singleindex quantile regression model and its estimation. R package for admm for penalized quantile regression. Bayesian quantile regression for singleindex models. Penalized regression methods for linear models in sas stat funda gunes, sas institute inc. Whereas the method of least squares estimates the conditional mean of the response variable across values of the predictor variables, quantile regression estimates the conditional median or other quantiles. A single index quantile regression model and its estimation efang kong university of kent yingcun xia nanjing university and national university of singapore models with single index. Gee analysis for longitudinal singleindex quantile regression. Estimation and variable selection for quantile partially.
This is an advancement from the existing quantile regression methods for the highdimensional sparse model. The fitting method implements the lasso penalty of tibshirani for fitting quantile regression models. Quantile regression for singleindexcoefficient regression models. This paper is concerned with quantile regression for a semiparametric regression model, in which both the conditional mean and conditional variance function of the response given the covariates admit a single index structure. Penalized singleindex quantile regression alkenani. This paper considers weighted composite quantile estimation of the single index model with missing covariates at random.
Penalized least squares for single index models heng penga,1, tao huangb,2 a department of mathematics, hong kong baptist university, kowloon tong, hong kong b department of statistics, university of virginia, charlottesville, va 22904, united states. Penalized quantile regression for lasso, scad, and mcp penalty. This paper is concerned with the estimation and variable selection for partially linear single index quantile regression models. We propose a penalized quantile regression and an independence screen.
In such models, the overall number of regressors p is very large, possibly much larger than the sample size n. Local influence analysis for penalized gaussian likelihood estimation in partially linear single index models, annals of the institute of statistical mathematics, springer. Quantile regression selection jmp software from sas. We start by considering a single index quantile regression model, which assumes that the conditional quantile depends on x through a single linear combination of the predictors, then extend to a. Pdf bayesian quantile regression for singleindex models. Onestep sparse estimates in nonconcave penalized likelihood mod els. As a result of this the group lasso penalty is the same as the typical lasso penalty and thus you should only use a scad or mcp penalty. Regularized quantile regression and robust feature screening for. Quantile regression and variable selection of partial linear single index model, annals of the institute of statistical mathematics, springer. Single index models offer greater flexibility in data analysis than linear models but retain. What is penalized logistic regression cross validated. Sorry, we are unable to provide the full text but you may find it at the following locations. Under some regularity conditions, we establish the large sample properties of the estimated index. Two step composite quantile regression for single index.
However, it is possible that there are many unimportant predictors within the original predictors. Distance correlation, penalized quantile regression, singleindex models, sure. Abstract we propose a semismooth newton coordinate descent sncd algorithm for elasticnet penalized robust regression. Semismooth newton coordinate descent algorithm for elasticnet penalized huber loss and quantile regression congrui yi and jian huang department of statistics and actuarial science university of iowa iowa city, ia 52242 u. The recently proposed method of weighted quantile sum wqs regression attempts to overcome these problems by estimating a body burden index, which identifies important chemicals. Quantile regression and variable selection for the single. Estimating quantile regression models for independent and hierarchical data with r marco geraci mrc centre of epidemiology for child health institute of child health, university college london m. Quantile regression extends the regression model to conditional quantiles. Quantile regression of partial linear single index. To demonstrate the robustness of quantile regression to outlying observations, we consider data from central bank of nigeria, with the quarterly implicit price deflator as the dependent variable, and agriculture, industry, building and construction, wholesale and retail, services, as independent variables. For single index coefficient models, 20 considered a new estimation pro. Quantile regression and variable selection for partially. Since in this case the ordinary quantile regression is not consistent, we consider quantile regression penalized by the 1norm of coefficients l1qr. The resulting estimators have the asymptotic normality and achieve the best convergence rate.
Partially linear additive quantile regression in ultrahigh dimension sherwood, ben and wang, lan, the annals of statistics, 2016. The performance of the proposed method is investigated through simulation studies and a real data example. To reduce the dimensionality while still retaining the flexibility of a nonparametric model, we propose modeling the conditional quantile by a single index. Whereas the method of least squares estimates the conditional mean of the response variable across values of the predictor variables, quantile regression estimates the conditional median or other quantiles of the response variable. L1penalized quantile regression in highdimensional. Partially linear single index models are flexible dimension reduction semiparametric tools yet still retain ease of interpretability as linear models. While quantile regression can be seen as a generalization of median regression, expectiles as alternative are a generalized form of mean regression. In the proposed method, the bayesian elastic net is suggested for single index quantile regression for estimation and variables selection. Penalized quantile regression 83 in this paper, we consider quantile regression in highdimensional sparse models hdsms.
The goal of regression analysis amounts to characterizing how the. Highdimensional varying index coefficient quantile regression model. Kong and xia 25 combined quantile regression and a penalty function to develop an adaptive. Applications with heterogeneous preferences this paper proposes new 1penalized quantile regression estimators for panel data, which explicitly allows for individual heterogeneity associated with covariates. Quantile regression is a type of regression analysis used in statistics and econometrics. L1penalized quantile regression in highdimensional sparse. In set up ii and iii, the penalized quantile regression at single quantile level tends to miss relevant variables when the target quantile level is outside of the quantile index range, where these covariates. Using an asymmetric laplace distribution, which provides a mechanism for bayesian inference of quantile regression models, we develop a fully bayesian approach to fitting single index models in conditional quantile regression.
Quantile regression and variable selection for partially linear single index models with missing censoring indicators. Penalized spline estimation for partially linear singleindex mod. Regularized quantile regression and robust feature screening for single index models wei zhong, liping zhu, runze li and hengjian cui xiamen university, shanghai university of finance and economics pennsylvania state university and capital normal university abstract. In such models, the overall number of regressors p is very. The base year of the data set i found from the imf is 2010. Inference for singleindex quantile regression models with. We propose both a penalized quantile regression and an independence. Linear quantile regression is related to linear leastsquares regression in that both are interested in studying the linear relationship between a response variable and one or more independent or explanatory variables. Penalized likelihood regression for generalized linear models with nonquadratic penalties.
To reduce the dimensionality while still retaining the flexibility of a nonparametric model, we propose modeling the conditional quantile by a singleindex function g 0 x t. Penalized spline estimation for partially linear singleindex. Penalized spline estimation for partially linear single index models. Semismooth newton coordinate descent algorithm for. Then range of lambdas goes from the maximum lambda found to eps on the log scale. Covar, which is the change of value at risk var of the financial system conditional on an institution being under distress compared to median state. We consider median regression and, more generally, a possibly infinite collection of quantile regressions in highdimensional sparse models. Single index models offer greater flexibility in data analysis than linear models but retain some of the desirable properties such as the interpretability of the coefficients. Penalized quantile regression with semiparametric correlated. Annals of the institute of statistical mathematics, vol. Penalized regression methods for linear models in sasstat. We consider a pseudoprofile likelihood approach to estimation and testing for single index quantile regression models. Produces penalized quantile regression models for a range of lambdas and penalty of choice. Weighted composite quantile regression for single index.
It is important to note that the penalized quantile regression. Five things you should know about quantile regression. Notice that the loss function used in quantile regression is. Ordinary least squares regression models the relationship between one or more covariates x and the conditional mean of the response variable y given xx. Fits a quantile regression model with the lasso penalty. We consider a pseudoprofile likelihood approach to estimation and testing for single index quantile regression. Annals of the institute of statistical mathematics. Quantile regression extends the regression model to conditional quantiles of the response variable, such as the 90th percentile.
If lambda is unselected than an iterative algorithm is used to find a maximum lambda such that the penalty is large enough to produce an intercept only model. A practical algorithm and the asymptotic properties of the proposed estimators are established. Quantile regression and variable selection of singleindex. Single index models offer greater flexibility in data analysis than linear. It wraps up both qradm and qpadmm into a single package. To our limited knowledge, there still lacks of study on variable selection in penalized quantile regression. In these models, the number of regressors p is very large, possibly larger than the sample size n, but only at most s regressors have a nonzero impact on each conditional quantile of the response variable, where s grows more slowly than n. Generally, quantiles provide a natural interpretation even beyond the 0. Distance correlation, penalized quantile regression, single index models, sure screening property.
Quantile regression and variable selection of partial. I am a bit confused how to use the fourth variable, the index number in this multiple regression. Furthermore, we propose a variable selection procedure for the qr of sim by combining the estimation method with the adaptive lasso penalized method to. Penalized spline estimation for partially linear single. Basic concepts of quantile regression fitting quantile regression models building quantile regression models applying quantile regression. In addition, penalized regression methods designed to remediate collinearity may have limitations in selecting the truly bad actors among many correlated components. Index 47 rqpenpackage penalized quantile regression for lasso, scad, and mcp penalty functions including group penalties description this package provides functions to. Do i use the changes of the index in my regression, with log. Variable selection in quantile regression 3 with the adaptive lasso penalty. However, it is possible that there are many unimportant. Furthermore, a variable selection method is investigated for the qrsicm by combining macle method with the adaptive lasso. Regularized quantile regression and robust feature screening for single index.
Penalized least squares for single index models heng penga,1, tao huangb,2 a department of mathematics, hong kong baptist university, kowloon tong, hong kong b department of statistics. Mar 14, 2012 quantile regression and variable selection of partial linear single index model. One noteworthy point is that similar to the result in. Linear and nonlinear parametric and nonparametric total variation penalized models for conditional quantiles. Local linear approximation approach used by wang, wu and li. Please refer to the following two papers for details. These problems require you to perform statistical model selection to. Fourth, we analyze the rate of convergence of a twostep estimator that applies ordinary quantile regression to the selected model. Semiparametric quantile regression with highdimensional covariates liping zhu1. Quantile regression selection performs effect selection in the framework of quantile regression models. Adaptive penalized quantile regression for high dimensional data.
1126 710 882 219 76 1370 590 829 132 218 1355 784 598 697 600 1359 1520 39 1333 778 318 1002 1376 876 994 698 220 1207 330