Improved Parameter Estimation


Box, M.J.   (1970, ASQC and the American Statistical Association)   Central Instrument Research Laboratory, Pangbourne, Berks, England

Technometrics    Vol. 12    No. 2
QICID: 8176    May 1970    pp. 219-229
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Article Abstract

Box and Draper (1968) have considered the use of data with non-homogeneous variance in non-linear model-building, and have discussed in detail the problems of(i) parameter estimation(ii) the determination of a joint posterior probability region for these estimates(iii) the optimal selection of experiments for estimating the parameters, given the model.The present paper has two objectives: firstly to show that the assumption of a known non-constant variance-covariance structure for the experimental error is practically highly relevant, since it covers the situation in which(i) the so-called independent variables are subject to error(ii) the so-called response is not measured directly, but is computed from other prime variables which are actually measured(iii) the model is a relationship between a number of variables, possibly all subject to error, and which cannot be rigidly classified as response and independent variables;and secondly to show that in these situations it is possible to estimate the parameters using a general computer program in which the derivatives of the residuals with respect to the independent variables, which are needed to compute the effective variance-covariance matrices, are estimated numerically. This eliminates much tedious algebraic manipulation, and provides the user with a statistically advanced technique which is no more difficult to use than "least squares" estimation.

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