An improved monotone conditional quantile estimator (Q688395)

Suppose that \((X_ 1,Y_ 1),\dots, (X_ n,Y_ n)\) are i.i.d. bivariate random vectors and that \(\xi_ p(x)\) is the \(p\)-quantile of \(Y_ 1\) given \(X_ 1=x\) for \(0<p<1\). Estimation of \(\xi_ p(x)\), when it is monotone in \(x\), has been studied in the literature. In nonparametric conditional quantile estimation one uses only some smoothness assumptions. The asymptotic properties are superior in the latter case; however, monotonicity is not guaranteed. The author introduces a new estimator that enjoys both of the above properties.