Mathematical Sciences: A Robust Approach to the Prediction Problem

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The research from this proposal will create techniques that will enhance the way in which scientists predict responses from limited amounts of data. The techniques will be robust in nature thereby precluding unduly restrictive distributional assumptions. An approach will be taken similar to what has been done with confidence intervals: robust estimates of location and spread will be used to create prediction intervals for a function of a set of future observations. Recent advances in the field of adaptive estimation will also be used to classify the underlying distribution. This research will go far beyond currently available statistical methods for predicting responses. Statistical prediction will be developed for new types of data, types for which existing statistical methods have been used even though scientists knew they were misfit because no other methods existed. Since the ability to predict is vital to scientists and engineers, the results from this research will aid in advancing the state-of-the-art in a variety of fields.