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. Mar 17, 2012 read bayesian quantile regression for single index models, statistics and computing on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Although its computation requires linear programming methods, the quantile regression estimator is asymptotically normally distributed. Keywords single index partial linear quantile regression asymptotic normality minimizing average check loss estimation variable selection adaptive lasso 1 introduction semiparametric model has been popular in the literature recently due to the explana. This paper focuses on a single index model for the conditional quantile. Functional singleindex quantile regression models peijun sang jiguo cao received. A full range of quantile analysis can provide more complete.
The first step in estimating the single linear index selection equation uses ichimuras 1993 semiparametric procedure. Quantileestimationofa generalsingleindex model efangkong. Composite quantile regression for the singleindex model. 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. Models with single index structures are among the many existing popular semiparametric approaches for either the conditional mean or the conditional variance. Functional single index quantile regression models peijun sang jiguo cao received. In this paper, we introduce singleindex quantile regression for nonparametric. To reduce the dimensionality while still retaining the flexibility of a nonparametric model, we propose modeling the conditional quantile by a singleindex function, where a univariate link function g0dot operator is applied to a linear. The proposed estimation scheme is an extension of the full iteration procedure proposed by carroll et al. Jan 05, 2017 quantile regression is in the focus of many estimation techniques and is an important tool in data analysis. As an empirical study, we apply the single index quantile regression model to boston housing data. Rubinfeld 1978 based on a linear regression analysis.
Quantile regression is in the focus of many estimation techniques and is an important tool in data analysis. Quantile regression qr is becoming increasingly popular due to its relevance in many scientific investigations. Abstractsingle index model conditional quantile regression is proposed in order to overcome the dimensionality problem in nonparametric quantile regression. In the proposed method, the bayesian elastic net is suggested for single index quantile regression for estimation and variables selection. In this work, we consider the estimation of a semiparametric single index model for conditional quantiles with rightcensored data.
Request pdf a singleindex quantile regression model and its estimation models with singleindex structures are among the many existing popular. In this work, we consider the estimation of a semiparametric singleindex model for conditional quantiles with rightcensored data. Christopher f baum bc diw quantile regression boston college. 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. Dvine copula based quantile regression daniel kraus and claudia czadoy november 17, 2016 abstract quantile regression, that is the prediction of conditional quantiles, has steadily gained importance in statistical modeling and nancial applications. In real data analysis, the covariates of model 1 may include many irrelevant.
We consider a pseudoprofile likelihood approach to estimation and testing for single index quantile regression models. The main purpose of dvine copula based quantile regression is to predict the quantile of a response 1 d and d. Pdf bayesian quantile regression for singleindex models. Applied econometrics boston college, spring 20 christopher f baum bc diw quantile regression boston college, spring 20 1 20. As an example of data with this structure, consider the scatterplot in figure 1 of body mass index bmi against age for 8,250 men from a fouryear 19992002 survey by the national center for health statistics. Package quantreg april 1, 2020 title quantile regression description estimation and inference methods for models of conditional quantiles. Highdimensional varying index coefficient quantile regression model. One noteworthy point is that similar to the result in. A singleindex quantile regression model and its estimation volume 28 issue 4 efang kong, yingcun xia.
Read bayesian quantile regression for singleindex models, statistics and computing on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Composite quantile regression and variable selection 763 singleindex model sim see wu et al. We consider a pseudoprofile likelihood approach to estimation and testing for singleindex quantile regression models. We propose an adaptive estimation procedure and an iterative algorithm which, under mild regularity conditions, is proved to converge with. In this paper, we extend the composite quantile regression cqr method to a singleindex model. Composite quantile regression for the singleindex model by. Composite quantile regression and variable selection 763 single index model sim see wu et al. Using an asymmetric laplace distribution, which provides a mechanism for bayesian inference of quantile regression models, we develop a fully bayesian approach to fitting singleindex models in conditional quantile regression. In this work, we use a gaussian process prior for the unknown nonparametric link function and a laplace distribution on the index vector, with the latter motivated by. This paper focuses on the quantile regression qr estimation for the partially linear singleindex models where the data are right censored and the censoring indicators are missing at random. Submitted to the annals of statistics composite quantile regression for the single index model by yan fany,wolfgang karl hardle z,weining wangzand lixing zhux renmin university o. Quantileestimationofa generalsingleindex model arxiv.
Single index models offer greater flexibility in data analysis than linear models but retain some of the desirable properties such as the interpretability. The papers submitted to this special issue should deal with one or more of the following topics. We propose a projection based single index model specification. This paper focuses on a singleindex model for the conditional quantile. In this paper, we introduce singleindex quantile regression for nonparametric estimation with multivariate covariates. However, the performance of these models may be adversely affected by extremely large values or skewness in the. Linear and nonlinear parametric and nonparametric total variation penalized models for conditional quantiles of a univariate response and several methods for handling censored survival data. Singleindex quantile regression models for censored data. Technische universiteit eindhoven yingcunxia national university of singapore, singapore abstract the singleindex model is one of the most popular semiparametric models in econometrics. The unknown link function is estimated by local composite quantile regression and the. Regularized quantile regression and robust feature. When it comes to nonparametric specifications of the conditional quantile or more generally tail curve one faces, as in mean regression, a dimensionality problem.
However, the performance of these models may be adversely affected by extremely large values or skewness in the response. This study uses quantile regression techniques to analyze changes in the returns to education for women. Compared to mean regression, quantile regression for this class of models is more. We propose both a penalized quantile regression and an independence. Quantile regression and variable selection for partially linear singleindex models with missing censoring indicators.
Journal of multivariate analysis 101 2010 16071621. It is known that functional singleindex regression models can achieve better prediction accuracy than functional linear models or fully nonparametric models, when the target is to predict a scalar response using a functionvalued covariate. Regularized quantile regression and robust feature screening. Many widely used parametric models can be seen as particular cases of the singleindex model. Compared to mean regression, quantile regression for this class of models is more technically challenging and has not been considered before. Pdf using an asymmetric laplace distribution, which provides a mechanism for bayesian inference of quantile regression models, we. Models with singleindex structures are among the many existing popular semiparametric approaches for either the conditional mean or the conditional variance.
Abstractin this article, a new efficient iteration procedure based on quantile regression is developed for singleindex varyingcoefficient models. By considering different levels of quantile, we explore how the covariates, of either social or environmental nature, could have different effects on individuals targeting the low, the median, and the high end of the housing market. Quantile regression and variable selection for single. Quantile regression and variable selection for partially. Single index quantile regression for heteroscedastic data by. This display is used to diagnose both vertical outliers and horizontal leverage points. Single index quantile regression for heteroscedastic data. The advantage of using quantile regression is that the quantile function characterizes f at 1.
These considerations become even more important for incomplete data. By considering different levels of quantile, we explore how the covariates, of either social or environmental nature, could have different effects on individuals targeting the low, the median, and the high end of the. Quantile regression is a type of regression analysis used in statistics and econometrics. Submitted to the annals of statistics composite quantile regression for the singleindex model by yan fany,wolfgang karl hardle z,weining wangzand lixing. Functional singleindex quantile regression models springerlink. 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. However, it is possible that there are many unimportant predictors within the original predictors. We consider quantile regression incorporating polynomial spline approximation for single index coefficient models. Examples are the linear regression model and the generalized linear model. 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. 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. To reduce the dimensionality while still retaining the flexibility of a nonparametric model, we propose modeling the conditional quantile by a single index function g 0 x t.
Quantile regression and variable selection for the single. Keywords single index partial linear quantile regression. Quantile regression and variable selection of partial. Pdf singleindex quantile regression keming yu academia. In this paper, we extend the composite quantile regression cqr method to a single index model. As an example of data with this structure, consider the scatterplot in figure 1 of body mass index bmi against age for 8,250 men from a fouryear 19992002 survey. 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. We propose a projection based single index model specifi cation. The key terms in the analysis are thus the gradient and the hessian. To reduce the dimensionality while still retaining the flexibility of a nonparametric model, we propose modeling the conditional quantile by a single index function, where a univariate link function g0dot operator is applied to a linear. Linear and nonlinear qr models have been studied extensively, while recent research focuses on the single index quantile regression siqr model. 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 singleindex structure.
A singleindex quantile regression model and its estimation. Accuracy of the ultrasound estimate of the amniotic fluid volume amniotic fluid index and single deepest pocket to identify actual low, normal, and high amniotic fluid volumes as determined by quantile regression. Quantile regression and variable selection of singleindex. Accuracy of the ultrasound estimate of the amniotic fluid. Pdf quantile regression for the singleindex coefficient. However, there is no work for the sicm based on the quantile method. Abstractin this article, a new efficient iteration procedure based on quantile regression is developed for single index varyingcoefficient models. Bayesian quantile regression for singleindex models. To correct for an unknown form of a sample selection bias in the. The data used is the march current population survey for the years 1968, 1973, 1979, 1986 and 1990.
Inference for singleindex quantile regression models with. Median regression is more robust to outliers than least squares. Quantile regression minimizes a sum that gives asymmetric penalties 1 qjei jfor overprediction and qjei jfor underprediction. Online supplementary appendix c for \single index quantile regression for heteroscedastic data by eliana christou and michael g. Quantile regression and variable selection for singleindex. Quantile regression and variable selection of partial linear single. Iteratively applying the locallinear smoothing approach, we simultaneously estimate the linear coefficients and the link function. We consider quantile regression incorporating polynomial spline approximation for singleindex coefficient models. To reduce the dimensionality while still retaining the flexibility of a nonparametric model, we propose modeling the conditional quantile by a singleindex function g0xt.
The gaussian process prior is considered for unknown link function. 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. As an empirical study, we apply the singleindex quantile regression model to boston housing data. Diagnostics for the median regression fit, which are requested in the plots option, are displayed in output 100. The unknown link function is estimated by local composite quantile regression and the parametric. Bayesian elastic net single index quantile regression. The estimator of the link function converges at the usual rate for nonparametric estimation of a univariate function. 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. Singleindex composite quantile regression request pdf.
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