Statistical estimation and modeling with finite data

In this paper we present an approach for statistical modeling and estimation with finite data. This problem is motivated by the need to provide a framework for highly non-stationary situations where the complexity of the environment often exceeds the ability to collect meaningful data. In communication systems this situation arises when the coherence time is significant relative to the delay spread. Historically, statistical methods address this issue by appealing to the Ockham´s razor principle and this has led to several approaches which in general result in optimizing a combination of model complexity and empirical error for choosing estimates. Although these approaches provide meaningful estimates in the limit of large enough data, they are not applicable to finite data situations.