  We show that spline and wavelet series regression estimators for weakly
dependent regressors attain the optimal uniform (i.e. sup-norm) convergence
rate $(n/\log n)^{-p/(2p+d)}$ of Stone (1982), where $d$ is the number of
regressors and $p$ is the smoothness of the regression function. The optimal
rate is achieved even for heavy-tailed martingale difference errors with finite
$(2+(d/p))$th absolute moment for $d/p<2$. We also establish the asymptotic
normality of t statistics for possibly nonlinear, irregular functionals of the
conditional mean function under weak conditions. The results are proved by
deriving a new exponential inequality for sums of weakly dependent random
matrices, which is of independent interest.
