Non-crossing nonparametric estimates of quantile curves
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Date
2007-05-25T12:58:47Z
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Abstract
In this paper a new nonparametric estimate of conditional quantiles is proposed, that
avoids the problem of crossing quantile curves [calculated for various p ist Element von (0; 1)]: The method
uses an initial estimate of the conditional distribution function in a first step and solves the
problem of inversion and monotonization with respect to p ist Element von (0; 1) simultaneously. It is
demonstrated that the new estimates are asymptotically normal distributed and asymptotically first order equivalent to quantile estimates obtained by local constant or local linear
smoothing of the conditional distribution function. The performance of the new procedure is
illustrated by means of a simulation study and some comparisons with the currently available
procedures which are similar in spirit with the proposed method are presented.
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Keywords
Conditional distribution, Crossing quantile curves, Local linear estimate, Nadaraya Watson estimate, Quantile estimation