PREDICTING INTEGRALS OF STOCHASTIC PROCESSES

• 成果类型: Article
• 署名作者: Stein, Michael L.
• 署名单位: University of Chicago
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/aoap/1177004834
• 发表日期: 1995
• 页码: 158-170
• 关键词: regression problems; sampling designs

摘要

Consider predicting an integral of a stochastic process based on n observations of the stochastic process. Among all linear predictors, an optimal quadrature rule picks the n observation locations and the weights assigned to them to minimize the mean squared error of the prediction. While optimal quadrature rules are usually unattainable, it is possible to find rules that have good asymptotic properties as n -> infinity. Previous work has considered processes whose local behavior is like m-fold integrated Brownian motion for m a nonnegative integer. This paper obtains some asymptotic properties for quadrature rules based on median sampling for processes whose local behavior is not like m-fold integrated Brownian motion for any m.