Albers, C.J. and Schaafsma, W.
(2003).
Estimating a density by adapting an initial guess.
Computational Statistics and Data Analysis, 42(12) pp. 27–36.
Abstract
De Bruin et al. (Comput. Statist. Data Anal. 30 (1999) 19) provide a unique method to estimate the probability density f from a sample, given an initial guess ψ of f. An advantage of their estimate fn is that an approximate standard error can be provided. A disadvantage is that fn is less accurate, on the average, than more usual kernel estimates. The reason is that fn is not sufficiently smooth. As improvement, a smoothed analogue fn(m) is considered. The smoothing parameter m (the degree of a polynomial approximation) depends on the supposed quality of the initial guess ψ of f. Under certain conditions, the resulting density estimate fn(m) has smaller L1error, on the average, than kernel estimates with bandwidths based on likelihood crossvalidation. The theory requires that the initial guess is made up a priori. In practice, some data peeping may be necessary. The fn(m) provided look ‘surprisingly accurate’. The main advantage of fn(m) over many other density estimators is its uniqueness (when the procedures developed in this article are followed), another one is that an estimate is provided for the standard error of fn(m)
Item Type: 
Journal Article

ISSN: 
01679473 
Extra Information: 
Some of the symbols may not have transferred correctly into this bibliographic record. 
Keywords: 
density estimation; nonparametric methods 
Academic Unit/Department: 
Mathematics, Computing and Technology 
Item ID: 
5275 
Depositing User: 
Casper Albers

Date Deposited: 
14 Aug 2006 
Last Modified: 
02 Dec 2010 19:53 
URI: 
http://oro.open.ac.uk/id/eprint/5275 
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