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Abdelati Daouia, U. Toulouse 1
 Friday, 24 February 2012, 14:30 - 15:30

Abdelati Daouia, Université de Toulouse

On Projection-Type Estimators of Multivariate Isotonic Functions

Abstract:

Let $M$ be an isotonic real-valued function on a compact subset of $\mathbb{R}^d$ and let $\hat M_n$ be an unconstrained estimator of $M$.

A feasible monotonizing technique is to take the largest (smallest) monotone function that lies below (above) the estimator $\hat M_n$ or any convex combination of these two envelope estimators. When the process $r_n(\hat M_n - M)$ is asymptotically equicontinuous for some sequence $r_n>0$, we show that these projected estimators are $r_n$-equivalent in probability to the original unrestricted estimator.

Our first motivating application involves a monotone estimator of the conditional distribution function that has the distributional properties of the local linear regression estimator. Applications also include the estimation of econometric (probability-weighted moment, quantile-based) and biometric (mean remaining lifetime) functions.

Location: Plaine - Building NO - 9th floor salle des Professeurs
Contact: Jacqueline Bottemanne, This e-mail address is being protected from spam bots, you need JavaScript enabled to view it