منابع مشابه
On the Grenander Estimator at Zero.
We establish limit theory for the Grenander estimator of a monotone density near zero. In particular we consider the situation when the true density f(0) is unbounded at zero, with different rates of growth to infinity. In the course of our study we develop new switching relations using tools from convex analysis. The theory is applied to a problem involving mixtures.
متن کاملBootstrapping the Grenander estimator
Abstract: The goal of this paper is to study the bootstrap for the Grenander estimator. The first result is a proof of the inconsistency of the nonparametric bootstrap for the Grenander estimator at a given point. The second result is the development and verification of a bootstrap for the L1 confidence band for the Grenander estimator. As part of this work, kernel estimators are studied as alt...
متن کاملInconsistency of Bootstrap: the Grenander Estimator
In this paper we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate n 1 3 . The Grenander estimator, the nonparametric maximum likelihood estimator of an unknown nonincreasing density function f on [0,∞), is a prototypical example. We focus on this example and explore different approaches to cons...
متن کاملConvergence of Linear Functionals of the Grenander Estimator under Misspecification
Under the assumption that the true density is decreasing, it is well known that the Grenander estimator converges at rate n−1/3 if the true density is curved (Prakasa Rao, 1969) and at rate n−1/2 if the density is flat (Groeneboom and Pyke, 1983; Carolan and Dykstra, 1999). In the case that the true density is misspecified, the results of Patilea (2001) tell us that the global convergence rate ...
متن کاملAsymptotic Normality of the L K - Error of the Grenander Estimator
We investigate the limit behavior of the L k-distance between a decreasing density f and its nonparametric maximum likelihood es-timatorˆfn for k ≥ 1. Due to the inconsistency ofˆfn at zero, the case k = 2.5 turns out to be a kind of transition point. We extend asymp-totic normality of the L1-distance to the L k-distance for 1 ≤ k < 2.5, and obtain the analogous limiting result for a modificati...
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ژورنال
عنوان ژورنال: Statistica Sinica
سال: 2011
ISSN: 1017-0405
DOI: 10.5705/ss.2011.038a