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Abstract Details

Activity Number: 410
Type: Contributed
Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistics and the Environment
Abstract - #304708
Title: Prediction and Estimation of Random Fields
Author(s): Priya Kohli*+ and Mohsen Pourahmadi
Companies: Texas A&M University and Texas A&M University
Address: Department of Statistics, College Station, TX, 77843, United States
Keywords: Random Field ; Lattice ; Wold Decomposition ; Spectral Factorization ; Exponential Model

This paper presents several results for prediction of random fields defined on a rectangular lattice by extending the classical Kolmogorov-Wiener prediction theory of stationary processes. Using the multi-step ahead prediction errors and their variances, solutions are provided for a number of non-standard prediction problems which deals with the ``modified past'', when a finite number of observations are either added to or excluded from the past. These important and difficult prediction problems are closely related to the design issue or network site selection in the environmental, geostatistical and engineering applications. The proposed methodology is implemented by first fitting an exponential model to the spectrum and then using the recursive formulas which expresses the predictor coefficients in terms of the cepstrum coefficients of the process. A simulation study that investigates the predictive performance of the proposed methodology is included. The proposed framework is then applied to a data set of yields from an agricultural experiment.

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