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On Projection‐type Estimators of Multivariate Isotonic Functions
Author(s) -
DAOUIA ABDELAATI,
PARK BYEONG U.
Publication year - 2013
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2012.00815.x
Subject(s) - mathematics , estimator , quantile , minimax estimator , consistent estimator , isotonic regression , trimmed estimator , monotone polygon , efficient estimator , minimum variance unbiased estimator , projection (relational algebra) , statistics , algorithm , geometry
. 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 r n →∞, we show that these projection‐type 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) and biometric (mean remaining lifetime) functions.