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Predicting With Estimated Parameters

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Abstract

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.

Keywords

  • Spectral Density
  • Random Field
  • Gaussian Model
  • Fisher Information Matrix
  • Gaussian Random Field

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1999 Springer Science+Business Media New York

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Stein, M.L. (1999). Predicting With Estimated Parameters. In: Interpolation of Spatial Data. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1494-6_6

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  • DOI: https://doi.org/10.1007/978-1-4612-1494-6_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7166-6

  • Online ISBN: 978-1-4612-1494-6

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