  We consider parameter estimation for a linear parabolic second-order
stochastic partial differential equation (SPDE) in two space dimensions driven
by two types $Q$-Wiener processes based on high frequency data in time and
space. We first estimate the parameters which appear in the coordinate process
of the SPDE using the minimum contrast estimator based on the thinned data with
respect to space, and then construct an approximate coordinate process of the
SPDE. Furthermore, we propose estimators of the coefficient parameters of the
SPDE utilizing the approximate coordinate process based on the thinned data
with respect to time. We also give some simulation results.
