A neural model approach for regularization in the mean estimation case

Neural Networks are powerful tools for function approximation problems. A possible peculiar application of neural networks is that proposed here: estimating the univariate mean of a distribution from a finite sample. This problem characterizes a huge number of applicative and scientific problems. The Gaussian distribution case is analyzed, however the proposed analysis is of general validity and can be easily extended to other distributions. In particular the estimation problem is approached as a regularization problem and a solution to the selection of the regularization parameter is obtained via the employment of neural models. The paper, after introducing some theoretical results, presents two neural models, namely a MLP and a Circular Back Propagation Network, for the mean prediction. Experimental results show that neural networks can estimate the mean, in expectation, better than the usual sample mean formula.