Inference in dynamic error-in-variable-measurement problems

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 difficulty, 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 computationally 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.