TY - JOUR
T1 - Estimation of the reciprocal of the density quantile function at a point
AU - Babu, Gutti Jogesh
AU - Radhakrishna Rao, C.
N1 - Funding Information:
Received September 9, 1988; revised February 9, 1989. AMS 1980 subject classifications: primary 62FlO; secondary 62E20. Key words and phrases: kernel density estimation. location parameter family, quantile density function, quantile density estimation. * Research sponsored by the Air Force Office of Scientific Research under Grant AFSO-8% 0030. The U.S. Government’s right to retain a nonexclusive royalty-free license in and to the copyright covering this paper, for governmental purposes, is acknowledged.
PY - 1990/4
Y1 - 1990/4
N2 - Consistent estimators for the reciprocal of the density at a quantile point, which is the derivative of the quantile function, are considered. Rates of convergence of these estimators, depending on the smoothness properties of the density, are obtained. Two different, but natural, estimators of the reciprocal of the density at a quantile point, based on several samples from a location parameter family with unknown and possibly different location parameters are proposed. An important multivariate application is the estimation of the asymptotic dispersion matrix of several sample quantiles, as they involve reciprocals of the density at the corresponding population quantiles.
AB - Consistent estimators for the reciprocal of the density at a quantile point, which is the derivative of the quantile function, are considered. Rates of convergence of these estimators, depending on the smoothness properties of the density, are obtained. Two different, but natural, estimators of the reciprocal of the density at a quantile point, based on several samples from a location parameter family with unknown and possibly different location parameters are proposed. An important multivariate application is the estimation of the asymptotic dispersion matrix of several sample quantiles, as they involve reciprocals of the density at the corresponding population quantiles.
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U2 - 10.1016/0047-259X(90)90008-6
DO - 10.1016/0047-259X(90)90008-6
M3 - Article
AN - SCOPUS:38249019755
SN - 0047-259X
VL - 33
SP - 106
EP - 124
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - 1
ER -