Abstract. Extending the respective univariate result of Breuer and Major and of Giraitis and Surgailis, a vector process of shifted partial sums of a stationary short-range dependent sequence under instantaneous Gaussian subordination is shown to converge in distribution to the corresponding vector of independent Wiener processes. This result is then used to derive the asymptotic finite-dimensional distributions of kernel estimators of a regression function in a fixed-design nonparametric regression model with short-range dependent errors under Gaussian subordination. The asymptotic distributions of one- and two-sided maximal deviations of the kernel estimators over an increasingly finer grid are also determined when the short-range dependent errors in the model are normal.

AMS Subject Classification (1991): 62G07, 60F17

Received September 30, 1994, and in revised form March 17, 1995. (Registered under 5625/2009.)