Improved Estimation of Earth Rotation Parameters Using the Adaptive Ridge Regression

The multicollinearity among regression variables is a common phenomenon in the reduction of astronomical data. The phenomenon of multicollinearity and the diagnostic factors are introduced first. As a remedy, a new method, called adaptive ridge regression (ARR), which is an improved method of choosing the departure constant θ in ridge regression, is suggested and applied in a case that the Earth orientation parameters (EOP) are determined by lunar laser ranging (LLR). It is pointed out, via a diagnosis, the variance inflation factors (VIFs), that there exists serious multicollinearity among the regression variables. It is shown that the ARR method is effective in reducing the multicollinearity and makes the regression coefficients more stable than that of using ordinary least squares estimation (LS), especially when there is serious multicollinearity. This revised version was published online in July 2006 with corrections to the Cover Date.