On combining independent nonparametric regression estimators

Three estimators are investigated for linearly combining independent nonparametric regression estimators. Assuming fixed designs, the asymptotic mean squared errors and asymptotically optimal bandwidths are given for each estimator and compared. One estimator essentially ignores the differences in the sources and naively pools all of the data. The second utilizes individually optimized bandwidths and then estimates the best weights to combine them. The third estimator solves a general minimization problem and employs equal bandwidths and weights similar to those for combining unbiased estimators with unequal variance. It is found to be superior to the other two in most situations that would be encountered in practice.