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June, 1993 An Improved Monotone Conditional Quantile Estimator
Hari Mukerjee
Ann. Statist. 21(2): 924-942 (June, 1993). DOI: 10.1214/aos/1176349158

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.

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Hari Mukerjee. "An Improved Monotone Conditional Quantile Estimator." Ann. Statist. 21 (2) 924 - 942, June, 1993. https://doi.org/10.1214/aos/1176349158

Information

Published: June, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0789.62025
MathSciNet: MR1232526
Digital Object Identifier: 10.1214/aos/1176349158

Subjects:
Primary: 62G05
Secondary: 62G30

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 2 • June, 1993
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