Asymptotics of a Theil-type estimate in multiple linear regression

We present here, a proof based on the convexity lemma for the asymptotic distribution of a Theil-type estimate, based on Oja median for multiple linear regression model in the deterministic covariates case; in the iid random covariates case, a simple and short proof for the asymptotic distribution of the estimate is also included in this note. With an example of deterministic covariates case checked at the end of this note, we show this Theil-type estimate being more asymptotically efficient than the least absolute deviation estimate, in addition to its affine-invariance and robustness in small sample.