On estimates of regression coefficients

A class of linear unbiased estimates (including the least-squares ones) of regression coefficients for continuous parameter stochastic process (1) with stationary residual $\Delta(t)$ being considered, their asymptotic properties are studied. Theorem 1 gives a necessary and sufficient condition for these estimates to be consistent. In section 3 we study in more detail the asymptotic behaviour of correlation matrices. In theorem 2 the correlation matrix of the BLU estimates is evaluated. Restricting ourselves to spectral densities satisfying (2) we obtain conditions for the estimates to be asymptotically efficient (theorem 4). We show that the estimates considered can be successfully applied wh«n the least-squares ones are not good enough from the point of view of consistency and asymptotical efficiency.