Bootstrapping the generalized least-squares estimator in colored Gaussian noise with unknown covariance parameters

It is demonstrated that in problems involving the estimation of linear regression parameters in colored Gaussian noise, the simple least-squares estimator can be significantly suboptimal. When the noise covariance function can be described as a known function of a finite number of unknown nonrandom parameters, it is possible to take advantage of this information to improve upon the least-squares estimator by an appropriate bootstrapping technique. Two examples are given, and comments that may lead to other examples are presented.