A hierarchical approach to noise-adaptive estimation

This paper presents a noise-adaptive estimator for the linear model. The strategy is based on a hierarchical approach where in each step, a decreasing number of unbiased estimates for the parameter of interest is produced. In this way, the complexity is greatly reduced compared to standard estimators, like the adaptive maximum likelihood (AML) estimator. Also, since the method combines solutions to sub-problems of smaller dimensionality, the required size of the noise training data set is also reduced. As a result, the derived scheme performs better than AML for small sample support. The results are verified by simulations and show that the derived scheme is a very appropriate choice for a large class of problems with high dimensionality.