Theil-Type Estimate for Multiple Linear Regression 

Gang Shen


A Theil-type estimate for multiple linear regression models in the case 
of iid random covariates was proposed in Busarova et al (2006). It 
utilizes Oja spatial median on the elemental estimates of the regression 
coefficients. The essence of elemental estimate is that it transforms a 
regression problem into a location problem. This Theil-type estimate 
inherits affine-invariance and robustness in small sample. In this talk, 
I'll discuss this Theil-type estimate for the most interesting case, 
linear regression model with deterministic covariates, and its
asymptotic distribution. The asymptotic relative efficiency (ARE) of 
this estimate in an example of orthogonal design will be also compared 
with that of LSE, LAD.

Ref:
Asymptotics of a Theil-type estimate in multiple linear regression, 
(2009) Statistics and Probability Letters 79, 1053-1064.