Improved estimation of the stable laws |
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Authors: | P Besbeas B J T Morgan |
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Institution: | (1) Institute of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent, CT2 7NF, UK |
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Abstract: | 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. |
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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 |
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