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In this paper the problem of best linear unbiased estimation is investigatedfor continuous-time regression models. We prove several general statementsconcerning the explicit form of the best linear unbiased estimator (BLUE), inparticular when the error process is a smooth process with one or severalderivatives of the response process available for construction of theestimators. We derive the explicit form of the BLUE for many specific modelsincluding the cases of continuous autoregressive errors of order two andintegrated error processes (such as integrated Brownian motion). The resultsare illustrated by several examples.

Best linear unbiased estimators in continuous time regression models