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Abstract:
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A generalized, weighted multiple regression model with no intercept and equality-constrained coefficients is investigated and modified to arrive at best linear estimators (BLE) in direct support of subsurface mineral composition studies in oil exploration. Subsurface analyses have historically required use of a model relating a spectral response vector, Y, to a matrix of standard yields, X, for elemental standards such as iron, silicon, quartz, calcium, etc. A primary motivation for the resulting model approach is the need to more appropriately account for heteroscedasticity within the independent variables, which is prevalent in petroleum environments. Monte Carlo simulations are utilized to explore the performance of these estimators in the presence of measurement error and heteroscedasticity.
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