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Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

Daily Overview

Session

Contributions to Mathematical Statistics
Location: 1.002
Session Chair: Mathias Trabs

Presentation 1

Local polynomial estimation of quantile density functions

Niclas Jacobsen, Natalie Neumeyer

University of Hamburg, Germany

A new approach for nonparametric estimation of quantile density functions based on
local polynomial estimation is presented. Estimation of the quantile density is important
because it appears for example in the expression for the asymptotic variance of empirical
and kernel type estimators of the quantile function.

The new approach uses a local polynomial regression on (F_n(X_i), Q_n(F_n(X_i))), where F_n
and Q_n represent the empirical distribution function and the empirical quantile function
respectively.

The new approach has more advantageous properties at the boundary than classical quan-
tile density estimators. We present a result on the asymptotic normality of the proposed
estimator. In this context we also get the leading bias term and the asymptotic variance,
which we use to compare the new estimator to classical estimators, especially focusing on
the boundary.

Keywords: asymptotic normality, bias rates, boundary adaptation, empirical quan-
tile function, nonparametric function estimator