scholarly journals Composite Quantile Regression for Varying Coefficient Models with Response Data Missing at Random

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1065 ◽  
Author(s):  
Shuanghua Luo ◽  
Cheng-yi Zhang ◽  
Meihua Wang
Keyword(s):  
Quantile Regression ◽  
Real Life ◽  
Missing At Random ◽  
Unknown Coefficient ◽  
Varying Coefficient Models ◽  
Test Procedures ◽  
Composite Quantile Regression ◽  
Varying Coefficient ◽  
Response Data ◽  
Data Missing

Composite quantile regression (CQR) estimation and inference are studied for varying coefficient models with response data missing at random. Three estimators including the weighted local linear CQR (WLLCQR) estimator, the nonparametric WLLCQR (NWLLCQR) estimator, and the imputed WLLCQR (IWLLCQR) estimator are proposed for unknown coefficient functions. Under some mild conditions, the proposed estimators are asymptotic normal. Simulation studies demonstrate that the unknown coefficient estimators with IWLLCQR are superior to the other two with WLLCQR and NWLLCQR. Moreover, bootstrap test procedures based on the IWLLCQR fittings is developed to test whether the coefficient functions are actually varying. Finally, a type of investigated real-life data is analyzed to illustrated the applications of the proposed method.

scholarly journals Robust estimation and inference for general varying coefficient models with missing observations

Test ◽  
2019 ◽  
Vol 29 (4) ◽  
pp. 966-988
Author(s):  
Francesco Bravo
Keyword(s):  
Nonlinear Least Squares ◽  
Missing At Random ◽  
Varying Coefficient Models ◽  
Finite Sample ◽  
Dimensional Parameter ◽  
Infinite Dimensional ◽  
Varying Coefficient ◽  
Finite Sample Properties ◽  
Local Linear Estimation ◽  
Nonlinear Least Squares Estimation

AbstractThis paper considers estimation and inference for a class of varying coefficient models in which some of the responses and some of the covariates are missing at random and outliers are present. The paper proposes two general estimators—and a computationally attractive and asymptotically equivalent one-step version of them—that combine inverse probability weighting and robust local linear estimation. The paper also considers inference for the unknown infinite-dimensional parameter and proposes two Wald statistics that are shown to have power under a sequence of local Pitman drifts and are consistent as the drifts diverge. The results of the paper are illustrated with three examples: robust local generalized estimating equations, robust local quasi-likelihood and robust local nonlinear least squares estimation. A simulation study shows that the proposed estimators and test statistics have competitive finite sample properties, whereas two empirical examples illustrate the applicability of the proposed estimation and testing methods.

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