In obtaining a regression tit to a set of data, ordinary least squares regression depends directly on the parametric model formulated by the researcher. Ifthis model is incorrect, a least squares analysis may be misleading. Altematively, nonparametric regression (kemel or local polynomial regression, for example) has no dependence on an underlying parametric model, but instead depends entirely on the distances between regressor coordinates and the prediction point of interest. This procedure avoids the necessity of a reliable model, but in using no information from the researcher, may Ht to irregular pattems in the data. The proper combination of these two regression procedures can overcome their respective problems. Considered is the situation where the researcher has an idea of which model should explain the behavior of the data, but this model is not adequate throughout the entire range of the data. An extension of partial linear regression and two methods of model robust regression are developed and compared in this context. These methods involve parametric tits to the data and nonparametric tits to either the data or residuals. The two tits are then combined in the most efficient proportions via a mixing parameter. Performance is based on bias and variance considerations.

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This article presents the application of a recently developed statistical regression method to the controlled instrument calibration problem. The statistical method of Model Robust Regression (MRR), developed by Mays, Birch, and Starnes, is shown to improve instrument calibration by reducing the reliance of the calibration on a predetermined parametric (e.g. polynomial, exponential, logarithmic) model. This is accomplished by allowing fits from the predetermined parametric model to be augmented by a certain portion of a fit to the residuals from the initial regression using a nonparametric (locally parametric) regression technique. The method is demonstrated for the absolute scale calibration of silicon-based pressure transducers. Nomenclature bBandwidth CCMSE Mean square error calculated using cross-check data dDegree of polynomial d.f.