ESTIMATING DENSITIES, QUANTILES, QUANTILE DENSITIES AND DENSITY QUANTILES

M. C. JONES

Department of Statistics, The Open University, Milton Keynes MK7 6AA, U.K.

(Received April 24, 1991; revised November 8, 1991)

Abstract. 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.

Key words and phrases: Kernel smoothing, reciprocal density, sparsity function.