Abstract #300783

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JSM 2002 Abstract #300783
Activity Number: 44
Type: Contributed
Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics*
Abstract - #300783
Title: The Least Concave Majorant of the Empirical Distribution Function
Author(s): Christopher Carolan*+
Affiliation(s): East Carolina University
Address: 129 Austin Hall, Greenville, North Carolina, 27858, USA
Keywords: Monotone density ; Concave distribution function ; Least concave majorant
Abstract:

Two estimators of a continuous, concave distribution function, with support over the positive halfline, are compared. The author provides stochastic bounds for errors, both pointwise and sup-norm, exhibited by the least concave majorant of the empirical distribution function as an estimate of the true distribution function in terms of samples from uniform distributions. The author offers evidence demonstrating the almost paradoxical result that the least concave majorant of the empirical distribution function performs better in terms of sup-norm error, as an estimator of the true distribution function, than does the emprical distribution function, yet performs worse as a pointwise estimator in terms of mean-squared error.

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