DENSITY-ESTIMATION IN THE L-INFINITY NORM FOR MIXING PROCESSES

Let X = (X(n), n epsilon N) be a strongly mixing or absolutely regular stationary stochastic process. We consider kernel-estimates of the de nsity of the marginal distribution of X(0). We focus on three modes of uniform convergence on compact subsets in R(d) : almost surely, in th e mean, in probability. In each case, the bounds reach an optimal orde r (that is the i.i.d.'s) for both mixing assumptions. The minimal rate s that guarantee these bounds in strong dependence and in absolute reg ularity frameworks are compared.