Consistent estimators for the reciprocal of the density at a quantile point are considered. Optimal rates of convergence of these estimators, depending on the smoothness properties of the density, are obtained. An symptotically efficient estimator sequence, in the mean square error sense, is found from among this class; unlike density estimators, these density quantile estimators do not require knowledge of the actual values of the density and its derivatives.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty