Gross-error detection plays a vital role in parameter estimation

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Efficient algorithms were developed for estimating model parameters from measured data, even in the presence of gross errors. In addition to point estimates of parameters, however, assessments of uncertainty are needed. Linear approximations provide standard errors, but they can be misleading when applied to models that are substantially nonlinear. To overcome this difficulg, profiling methods were developed for the case in which the regressor variables are error-free. These methods provide accurate nonlinear confidence regions, but become expensive for a large number of parameters. These profiling methods are modified to error-in-variable-measurement models with many incidental parameters. Laplace S method is used to integrate out the incidental parameters associated with the measurement errors, and then profiling methods are applied to obtain approximate confidence contours for the parameters. This approach is computa-tional& efficient, requires few function evaluations, and can be applied to large-scale problems, It is useful when certain measurement errors (such as input variables) are relatively small, but not so small that they can be ignored.We illustrate the effect of increasing input noise on approximation (Eq. 29) in a very simple situation. Consider a problem with only one state variable x, one incidental parameter u, and one parameter 0 where the measurements are given by