Group selection via adjusted weighted least absolute deviation regression

2020 ◽  
Vol 378 ◽  
pp. 112924
Author(s):  
Xiuli Wang ◽  
Zhimiao Cao ◽  
Chao Liu ◽  
Mingqiu Wang
Keyword(s):  
Group Selection ◽  
Least Absolute Deviation ◽  
Absolute Deviation ◽  
Least Absolute Deviation Regression

ASYMPTOTICALLY EFFICIENT MEDIAN REGRESSION IN THE PRESENCE OF HETEROSKEDASTICITY OF UNKNOWN FORM

2001 ◽  
Vol 17 (4) ◽  
pp. 765-784 ◽  
Author(s):  
Quanshui Zhao
Keyword(s):  
Least Squares Method ◽  
Generalized Least Squares ◽  
Least Absolute Deviation ◽  
Finite Sample ◽  
Median Regression ◽  
Absolute Deviation ◽  
Least Absolute Deviation Regression ◽  
Unknown Form ◽  
The One ◽  
Asymptotically Efficient

We consider a linear model with heteroskedasticity of unknown form. Using Stone's (1977, Annals of Statistics 5, 595–645) k nearest neighbors (k-NN) estimation approach, the optimal weightings for efficient least absolute deviation regression are estimated consistently using residuals from preliminary estimation. The reweighted least absolute deviation or median regression estimator with the estimated weights is shown to be equivalent to the estimator using the true but unknown weights under mild conditions. Asymptotic normality of the estimators is also established. In the finite sample case, the proposed estimators are found to outperform the generalized least squares method of Robinson (1987, Econometrica 55, 875–891) and the one-step estimator of Newey and Powell (1990, Econometric Theory 6, 295–317) based on a Monte Carlo simulation experiment.

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