Curvature Measures for Multiresponse Regression Models
将Bates & Watts针对单响应非线性最小二乘问题的曲率度量扩展到基于Box-Draper准则的多响应参数估计，通过广义最小二乘近似评估模型非线性程度。
The Bates & Watts (1981) curvature measures developed for single response nonlinear least squares problems are extended to multiresponse parameter estimation problems based on the Box-Draper estimation criterion. Exact determination contours are approximated by contours of the generalised least squares model conditioned on the maximum likelihood estimate of the covariance matrix for the responses. By this approximation, curvature measures calculated for the generalised least squares can be related to the determinant contours. The assessment of nonlinearity for a multiresponse model presented in this study is two-fold. First, a nonuniformity measure is developed to measure the validity of the approximation of the determinant contours by generalised least squares contours. Secondly, curvature measures similar to those of Bates & Watts are calculated for the generalised least squares model to evaluate the validity of the linear approximation of the model functions in a neighbourhood of the parameter estimates.