  Gaussian couplings of partial sum processes are derived for the
high-dimensional regime $d=o(n^{1/3})$. The coupling is derived for sums of
independent random vectors and subsequently extended to nonstationary time
series. Our inequalities depend explicitly on the dimension and on a measure of
nonstationarity, and are thus also applicable to arrays of random vectors. To
enable high-dimensional statistical inference, a feasible Gaussian
approximation scheme is proposed. Applications to sequential testing and
change-point detection are described.
