Improved estimation of the stable laws

Besbeas, Panagiotis and Morgan, Byron J. T. (2008) Improved estimation of the stable laws. Statistics and Computing, 18 (2). pp. 219-231. ISSN 0960-3174. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Fitting general stable laws to data by maximum likelihood is important but difficult. This is why much research has considered alternative procedures based on empirical characteristic functions. Two problems then are how many values of the characteristic function to select, and how to position them. We provide recommendations for both of these topics. We propose an arithmetic spacing of transform variables, coupled with a recommendation for the location of the variables. It is shown that arithmetic spacing, which is far simpler to implement, closely approximates optimum spacing. The new methods that result are compared in simulation studies with existing methods, including maximum-likelihood. The main conclusion is that arithmetic spacing of the values of the characteristic function, coupled with appropriately limiting the range for these values, improves the overall performance of the regression-type method of Koutrouvelis, which is the standard procedure for estimating general stable law parameters.

Item Type: Article
Uncontrolled keywords: arithmetic spacing; bounded influence; efficiency comparison; first zero; goodness-of-fit; k-L method; Koutrouvelis method; maximum-likelihood; robustness; testing for stability; transform variable selection
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Byron Morgan
Date Deposited: 27 Mar 2009 18:51
Last Modified: 09 May 2014 10:29
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