## The Annals of Statistics

### Asymptotic Properties of Weighted $L^2$ Quantile Distance Estimators

Vincent N. LaRiccia

#### Abstract

The asymptotic properties of a family of minimum quantile function distance estimators are considered. These procedures take as the parameter estimates that vector which minimizes a weighted $L^2$ distance between the empirical quantile function and an assumed parametric family of quantile functions. Regularity conditions needed for these estimators to be consistent and asymptotically normal are presented. For single parameter families of distributions, the optimal form of the weight function is presented.

#### Article information

Source
Ann. Statist., Volume 10, Number 2 (1982), 621-624.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345803

Digital Object Identifier
doi:10.1214/aos/1176345803

Mathematical Reviews number (MathSciNet)
MR653537

JSTOR
LaRiccia, Vincent N. Asymptotic Properties of Weighted $L^2$ Quantile Distance Estimators. Ann. Statist. 10 (1982), no. 2, 621--624. doi:10.1214/aos/1176345803. https://projecteuclid.org/euclid.aos/1176345803