Abstract #300474


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JSM 2002 Abstract #300474
Activity Number: 179
Type: Contributed
Date/Time: Tuesday, August 13, 2002 : 8:30 AM to 10:20 AM
Sponsor: General Methodology
Abstract - #300474
Title: Optimal Designs For Estimating the Path of a Stochastic Process
Author(s): Bhramar Mukherjee*+
Affiliation(s): University of Florida
Address: 226 Griffin Floyd Hall, Gainesville, Florida, 32611, USA
Keywords: product covariance structure ; integrated mean squared error ; exact sampling design ; Sacks-Ylvisaker regularity conditions
Abstract:

The problem of estimating a random process at unsampled points based on finitely many observations arises in communications theory, signal processing, and environmental sciences. We will focus on the related sampling design question of where to observe the process in order to attain "best" estimation accuracy in some suitable sense. For a special type of product covariance structure of the underlying stochastic process, conditions for exact optimality of the design points will be presented with integrated-mean squared error and maximum-mean squared error as the optimization criteria. The exact results lead to an interesting study of asymptotic optimality in the context of a larger class of processes satisfying natural regularity conditions proposed by Sacks and Ylvisaker (1966). Connection of this problem to Bayesian Numerical Analysis problems and problems in regression design with correlated error models will be indicated. Examples for standard processes will be presented.


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