In this paper the problem of best linear unbiased estimation is
investigated for continuous-time regression models. We prove several
general statements concerning the explicit form of the best linear unbiased
estimator (BLUE), in particular when the error process is a
smooth process with one or several derivatives of the response process
available for construction of the estimators. We derive the explicit
form of the BLUE for many specific models including the cases
of continuous autoregressive errors of order two and integrated error
processes (such as integrated Brownian motion). The results are
illustrated by several examples
