Shrinkage estimation for the mean of the inverse Gaussian population

We consider improved estimation strategies for a two-parameter inverse Gaussian distribution and use a shrinkage technique for the estimation of the mean parameter. In this context, two new shrinkage estimators are suggested and demonstrated to dominate the classical estimator under the quadratic risk with realistic conditions. Furthermore, based on our shrinkage strategy, a new estimator is proposed for the common mean of several inverse Gaussian distributions, which uniformly dominates the Graybill-Deal type unbiased estimator. The performance of the suggested estimators is examined by using simulated data and our shrinkage strategies are shown to work well. The estimation methods and results are illustrated by two empirical examples.