  A new modification of the minimum-contrast estimator (the weighted MCE) of
drift parameter in a linear stochastic evolution equation with additive
fractional noise is introduced in the setting of the spectral approach (Fourier
coordinates of the solution are observed). The reweighing technique, which
utilizes the self-similarity property, achieves strong consistency and
asymptotic normality of the estimator as number of coordinates increases and
time horizon is fixed (the space consistency). In this respect, this
modification outperforms the standard (non-weighted) minimum-contrast
estimator. Compared to other drift estimators studied within spectral approach
(eg. maximum likelihood, trajectory fitting), the weighted MCE is rather
universal. It covers discrete time as well as continuous time observations and
it is applicable to processes with any value of Hurst index $H \in (0,1)$. To
the author's best knowledge, this is so far the first space-consistent
estimator studied for $H < 1/2$.
