**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. |