Weak consistency and weak square root n-consistency of the ridge least weighted squares

Abstract

The regression method ridge least weighted squares (RLWS) was presented in [4] as a method which can handle multicollinearity as well as contamination simultaneously. This estimator combines the principles of the ridge regression and the least weighted squares (LWS) proposed in [10].

The normal equations for LWS and RLWS do not differ so much, thus we can use profitably the results of LWS consistency already presented in [12] and [13]. Therefore, it is possible to prove weak consistency and also weak square root n-consistency of RLWS in spite of the fact that the RLWS estimate is biased.

All results are proven under heteroscedasticity

Keywords

• Ridge least weighted squares
• consistency
• square root n-consistency
• heteroscedasticity.