scholarly journals Variable selection for non-parametric quantile regression via smoothing spline analysis of variance

Stat ◽  
2013 ◽  
Vol 2 (1) ◽  
pp. 255-268 ◽  
Author(s):  
Chen-Yen Lin ◽  
Howard Bondell ◽  
Hao Helen Zhang ◽  
Hui Zou
Keyword(s):  
Variable Selection ◽  
Quantile Regression ◽  
Analysis Of Variance ◽  
Smoothing Spline ◽  
Selection For ◽  
Non Parametric

Variable selection for ultra-high dimensional quantile regression with missing data and measurement error

2020 ◽  
pp. 096228022094153
Author(s):  
Yongxin Bai ◽  
Maozai Tian ◽  
Man-Lai Tang ◽  
Wing-Yan Lee
Keyword(s):  
Missing Data ◽  
Measurement Error ◽  
Variable Selection ◽  
Quantile Regression ◽  
Measurement Errors ◽  
Estimation Method ◽  
High Dimensional ◽  
Data Set ◽  
Cancer Data ◽  
Selection For

In this paper, we consider variable selection for ultra-high dimensional quantile regression model with missing data and measurement errors in covariates. Specifically, we correct the bias in the loss function caused by measurement error by applying the orthogonal quantile regression approach and remove the bias caused by missing data using the inverse probability weighting. A nonconvex Atan penalized estimation method is proposed for simultaneous variable selection and estimation. With the proper choice of the regularization parameter and under some relaxed conditions, we show that the proposed estimate enjoys the oracle properties. The choice of smoothing parameters is also discussed. The performance of the proposed variable selection procedure is assessed by Monte Carlo simulation studies. We further demonstrate the proposed procedure with a breast cancer data set.

scholarly journals Quantile regression and variable selection for partially linear model with randomly truncated data

2017 ◽  
Vol 60 (4) ◽  
pp. 1137-1160 ◽  
Author(s):  
Hong-Xia Xu ◽  
Zhen-Long Chen ◽  
Jiang-Feng Wang ◽  
Guo-Liang Fan
Keyword(s):  
Variable Selection ◽  
Quantile Regression ◽  
Linear Model ◽  
Partially Linear Model ◽  
Truncated Data ◽  
Partially Linear ◽  
Selection For

scholarly journals Mixed effect modelling and variable selection for quantile regression

2021 ◽  
pp. 1471082X2110334
Author(s):  
Haim Bar ◽  
James G. Booth ◽  
Martin T. Wells
Keyword(s):  
Variable Selection ◽  
Em Algorithm ◽  
Quantile Regression ◽  
Weighted Least Squares ◽  
Age At Onset ◽  
Real Data ◽  
Riboflavin Production ◽  
Mixed Effect ◽  
Linear Predictor ◽  
Selection For

It is known that the estimating equations for quantile regression (QR) can be solved using an EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent generalized inverse-Gaussian variables. This fact is exploited here to extend QR to allow for random effects in the linear predictor. Convergence of the algorithm in this setting is established by showing that it is a generalized alternating minimization (GAM) procedure. Another modification of the EM algorithm also allows us to adapt a recently proposed method for variable selection in mean regression models to the QR setting. Simulations show that the resulting method significantly outperforms variable selection in QR models using the lasso penalty. Applications to real data include a frailty QR analysis of hospital stays, and variable selection for age at onset of lung cancer and for riboflavin production rate using high-dimensional gene expression arrays for prediction.

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