Inference in Dynamic Error-in-Variable-Measurement Problems

Joao Albuquerque, Lorenz T. Biegler and Robert E. Kass


Efficient algorithms have been 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 these can be misleading when applied to models that are substantially nonlinear. To overcome this difficulty, ``profiling'' methods have been developed for the case in which the regressor variables are error free. In this paper we extend profiling methods to Error-in-Variable-Measurement (EVM) models. We use Laplace's method to integrate out the incidental parameters associated with the measurement errors, and then apply profiling methods to obtain approximate confidence contours for the parameters. This approach is computationally efficient, requiring few function evaluations, and can be applied to large scale problems. It is useful when the certain measurement errors (e.g., input variables) are relatively small, but not so small that they can be ignored.

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