Efficient Estimation of Some Elliptical Copula Regression Models through Scale Mixtures of Normal

2012 ◽  
Author(s):  
Nuttanan Wichitaksorn ◽  
Richard H. Gerlach ◽  
Boris Choy
Keyword(s):  
Regression Models ◽  
Efficient Estimation ◽  
Scale Mixtures ◽  
Elliptical Copula

scholarly journals EFFICIENT REGRESSIONS VIA OPTIMALLY COMBINING QUANTILE INFORMATION

2014 ◽  
Vol 30 (6) ◽  
pp. 1272-1314 ◽  
Author(s):  
Zhibiao Zhao ◽  
Zhijie Xiao
Keyword(s):  
Upper Bound ◽  
Regression Models ◽  
Statistical Estimation ◽  
Asymptotic Variance ◽  
Fixed Number ◽  
Efficient Estimation ◽  
Superior Performance ◽  
Quantile Regressions ◽  
Monte Carlo Experiments ◽  
Combining Information

We develop a generally applicable framework for constructing efficient estimators of regression models via quantile regressions. The proposed method is based on optimally combining information over multiple quantiles and can be applied to a broad range of parametric and nonparametric settings. When combining information over a fixed number of quantiles, we derive an upper bound on the distance between the efficiency of the proposed estimator and the Fisher information. As the number of quantiles increases, this upper bound decreases and the asymptotic variance of the proposed estimator approaches the Cramér–Rao lower bound under appropriate conditions. In the case of nonregular statistical estimation, the proposed estimator leads to super-efficient estimation. We illustrate the proposed method for several widely used regression models. Both asymptotic theory and Monte Carlo experiments show the superior performance over existing methods.

Linear censored regression models with scale mixtures of normal distributions

2015 ◽  
Vol 58 (1) ◽  
pp. 247-278 ◽  
Author(s):  
Aldo M. Garay ◽  
Victor H. Lachos ◽  
Heleno Bolfarine ◽  
Celso R. B. Cabral
Keyword(s):  
Regression Models ◽  
Censored Regression ◽  
Normal Distributions ◽  
Scale Mixtures ◽  
Censored Regression Models ◽  
Mixtures Of Normal Distributions
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