Jones, M. C.
Estimating densities, quantiles, quantile densities and density quantiles.
Annals of the Institute of Statistical Mathematics, 44(4) pp. 721–727.
To estimate the quantile density function (the derivative of the quantile function) by kernel means, there are two alternative approaches. One is the derivative of the kernel quantile estimator, the other is essentially the reciprocal of the kernel density estimator. We give ways in which the former method has certain advantages over the latter. Various closely related smoothing issues are also discussed.
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