  We propose a model with few parameters, for vacancy-induced ferromagnetism
based on a correlated model for anions (oxygen orbitals) with random potentials
that represent cation vacancies. There is a range of potential strength for
which moments appear on oxygen sites neighboring the vacancies. By using
techniques which allow us to treat the randomness exactly, we calculate the
magnetic couplings between the total moment around each vacancy, the Curie
temperature and dynamical correlations as a function of the effective stren gth
of the vacancy potential and doping properties, the density of vacancies, as
well as the correlation and band width of the host. For physically reasonable
parameters this predicts Curie temperatures well above room temperature for
small concentrations of vacancies and appropriate parameters. We disc uss our
results in relation to questions of stability and reproducibility raised in
experiments. To circumvent the difficulties of controlling intrinsic defects,
we propose specific non-magnetic host doping that could be, for example,
substituted for cations in HfO$_2$ or ZrO$_2$.
