A likelihood ratio test for bimodality in two-component mixtures with application to regional income distribution in the EU |
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Authors: | Hajo Holzmann Sebastian Vollmer |
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Institution: | 1.Institut für Stochastik,Universit?t Karlsruhe,Karlsruhe,Germany;2.Ibero-Amerika Institut für ?konomische Forschung und Institut für Statistik und ?konometrie,Universit?t G?ttingen,G?ttingen,Germany |
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Abstract: | We propose a parametric test for bimodality based on the likelihood principle by using two-component mixtures. The test uses
explicit characterizations of the modal structure of such mixtures in terms of their parameters. Examples include the univariate
and multivariate normal distributions and the von Mises distribution. We present the asymptotic distribution of the proposed
test and analyze its finite sample performance in a simulation study. To illustrate our method, we use mixtures to investigate
the modal structure of the cross-sectional distribution of per capita log GDP across EU regions from 1977 to 1993. Although
these mixtures clearly have two components over the whole time period, the resulting distributions evolve from bimodality
toward unimodality at the end of the 1970s. |
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Keywords: | Bimodality Convergence analysis Cross-sectional income distribution Likelihood ratio test Finite mixture |
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