Mathematical Sciences: A Robust Approach to the Prediction Problem

这项提案的研究将创造出一些技术，这些技术将增强科学家从有限的数据中预测反应的方式。这些技术在本质上是稳健的，从而排除了不适当的限制性分布假设。将采用一种类似于对置信区间所做的方法：将使用对位置和传播的稳健估计来为一组未来观测值的函数创建预测区间。自适应估计领域的最新进展也将用于对底层分布进行分类。这项研究将远远超出目前可用的预测反应的统计方法。统计预测将用于新类型的数据，这些数据已经使用了现有的统计方法，尽管科学家们知道它们不适合，因为没有其他方法存在。由于预测能力对科学家和工程师至关重要，因此这项研究的结果将有助于推动各个领域的最新技术。

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.