Predicting With Estimated Parameters
Chapters 3 and 4 examined the behavior of pseudo-BLPs. Although the results given there provide an understanding of how linear predictors depend on the spectral density of a stationary random field, they do not directly address the more practically pertinent problem of prediction when parameters of a model must be estimated from the same data that are available for prediction. The reason I have avoided prediction with estimated parameters until now is that it is very hard to obtain rigorous results for this problem. The basic difficulty is that once we have to estimate any parameters of the covariance structure, “linear” predictors based on these estimates are no longer actually linear since the coefficients of the predictors depend on the data.
KeywordsSpectral Density Random Field Gaussian Model Fisher Information Matrix Gaussian Random Field
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