Optimal convergence rates of nonparametric conditional quantiles in dependent cases (Q1895524)

Performance of statistical estimators often depends very much on model assumptions. It is desirable to see that optimal rates of convergence remain valid if there is some dependence structure in the data sequence. This note relaxes the independence assumption on the stationary sequence \(\{X_i, Y_i\}\). If the true conditional quantile function is smooth up to order \(r\) and the observed sequence is \(\beta\)-mixing (or absolutely regular), it is shown, under suitable mixing conditions, that the optimal global convergence rates can be achieved by the \(B\)-spline based estimators and their derivatives.