Scaled ridge estimator and its application to multimodel ensemble approaches for climate prediction

We propose a new regularized estimator called the scaled ridge estimator. The scaled ridge estimator is a modified version of the ridge estimator devised to reduce the bias of the ridge estimator by multiplying a positive constant to the ridge estimator. We show theoretically as well as numerically that the scaled ridge estimator performs better than the ridge estimator when the covariates are highly correlated and the true regression coefficients are similar. A motivational example is an ensemble approach for climate prediction based on the global circulation model. By analyzing data sets of monthly precipitation of 10 cites in South Korea, we illustrate that the scaled ridge estimator is a useful and efficient alternative to other competitors for ensemble climate prediction.