On Projection‐type Estimators of Multivariate Isotonic Functions |
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Authors: | ABDELAATI DAOUIA BYEONG U PARK |
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Institution: | 1. Institute of Statistics, Université catholique de Louvain and Toulouse School of Economics, University of Toulouse;2. Department of Statistics, Seoul National University |
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Abstract: | Abstract. Let M be an isotonic real‐valued function on a compact subset of and let be an unconstrained estimator of M. A feasible monotonizing technique is to take the largest (smallest) monotone function that lies below (above) the estimator or any convex combination of these two envelope estimators. When the process is asymptotically equicontinuous for some sequence rn→∞, we show that these projection‐type estimators are rn‐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) and biometric (mean remaining lifetime) functions. |
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Keywords: | asymptotic equicontinuity conditional distribution function frontier modelling isotonic limit process local linear fitting |
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