THE BLOCKWISE BOOTSTRAP FOR GENERAL EMPIRICAL PROCESSES OF STATIONARY-SEQUENCES

We apply the blockwise bootstrap for stationary observations, proposed by Kunsch (1989), to empirical processes indexed by function classes F which satisfy some bracketing conditions. We prove a bootstrap central limit theorem for empirical processes of stationary beta-mixing variables, which holds almost surely. This is done under a moment condition for the envelope function of F and by assuming an exponential decay of the mixing coefficients. By using exponential inequalities we apply a chaining technique.