## The Annals of Statistics

### An Improved Monotone Conditional Quantile Estimator

Hari Mukerjee

#### Abstract

Suppose that $(X_1, Y_1),\cdots, (X_n, Y_n)$ 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 the nonparametric conditional quantile estimation one uses only some smoothness assumptions. The asymptotic properties are superior in the latter case; however, monotonicity is not guaranteed. We introduce a new estimator that enjoys both of the above properties.

#### Article information

Source
Ann. Statist., Volume 21, Number 2 (1993), 924-942.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176349158

Digital Object Identifier
doi:10.1214/aos/1176349158

Mathematical Reviews number (MathSciNet)
MR1232526

Zentralblatt MATH identifier
0789.62025

JSTOR