A likelihood ratio test for bimodality in two-component mixtures with application to regional income distribution in the EU

Holzmann, Hajo; Vollmer, Sebastián

doi:10.1007/s10182-008-0057-2

Cited by 47 publications

(48 citation statements)

References 25 publications

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“…In 2001 the hypothesis of unimodality can only be rejected at the 10% level, from 2002 on it cannot be rejected anymore. We confirm these results using the recently introduced likelihood ratio test for bimodality in twocomponent normal mixture models in mean and variance by Holzmann and Vollmer (2008). The corresponding p values are shown in column p HV .…”

Section: Repeatsupporting

confidence: 69%

Distribution dynamics of regional GDP per employee in unified Germany

et al. 2011

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We investigate to what extent convergence in production levels per worker has been achieved in Germany since unification. To this end, we model the distribution of GDP per employee across German districts using two-component normal mixtures. While in the first year after unification, the two-component distributions were clearly separated and bimodal, corresponding to the East and West German districts, respectively, in the following years they started to merge showing only one mode. Still, using the recently developed EM-test for homogeneity in normal mixtures, the hypothesis of just a single normal component for the whole distribution is clearly rejected for all years. A Posterior analysis shows that about a third of the East German districts were assigned to the richer component in 2006, thus catching up to levels of the West. The growth rate of a mover district is about 1% point higher than the growth rate of a non-mover district which had the same initial level of GDP per employee.

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Section: Repeatsupporting

confidence: 69%

Distribution dynamics of regional GDP per employee in unified Germany

et al. 2011

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“…The null hypothesis is bimodality. Based on simulation results Holzmann, and Vollmer (2008) conclude that the LR test outperforms slightly the Silverman's test while both tests outperform the Dip test when the density is symmetric and bimodal. When the density is asymmetric and bimodal the LR test outperforms Silverman's test.…”

Section: Copyright C 2014 University Of Perugia Electronic Press Allmentioning

confidence: 99%

“…Following Holzmann, and Vollmer (2008) we consider f (z; θ) θ ∈ Θ ⊂ R d be a parametric family of densities allowing for the two component mixture family namely,…”

Section: Copyright C 2014 University Of Perugia Electronic Press Allmentioning

confidence: 99%

“…We follow Henderson et al (2008), Silverman (1981Silverman ( , 1986 and Holzmann, and Vollmer (2008) and employ modality tests to investigate the properties of the cross-sectional regional ethnicity level income distributions as proxied by the per capita CO2 emissions calculated for each historical ethnic homeland for all the decades starting from 1850 until 2005. Calibration methods are also employed to avoid small sample biases.…”

Section: Introductionmentioning

confidence: 99%

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Historical Ethnic Homelands and Income Convergence in Africa

Christopoulos

Mimis

Siourounis³

2014

Review of Economics and Institutions

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This paper tests the cross-sectional income convergence in historical African ethnic homelands proxied by per capita CO2 emissions between 1850 and 2005 using both parametric and non-parametric tests of cross-sectional income distribution modality. We report that the cross-sectional income distribution in historical African ethnic homelands exhibits two very persistent steady states: one very low and one medium-to-high. Excluding from the analysis those areas that had no CO2 emissions throughout the sample period -although they were inhabited -we find that ethnic homeland areas still share two distinct steady states after the 1940s. Our study contributes to the literature on income convergence in ethnically divergent areas and more specifically in the historical ethnic homelands in the African continent.

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“…If two-component mixtures under suitable parameter restrictions allow at most two modes, such as two-component normals with proportional covariances, or t-mixtures with equal degrees of freedom and covariances, one can use parametric methods to test for one against two modes in such a model by likelihood-ratio based methods, see Holzmann and Vollmer (2008) for univariate normal and von Mises mixtures. This requires explicit characterizations of the parameter constellations which yield unimodal or bimodal mixtures.…”

Section: Mclachlan Andmentioning

confidence: 99%

On the Number of Modes of Finite Mixtures of Elliptical Distributions

Alexandrovich

Holzmann

Ray

2013

Algorithms From and for Nature and Life

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We extend the concept of the ridgeline from Ray and Lindsay (2005) to finite mixtures of general elliptical densities with possibly distinct density generators in each component. This can be used to obtain bounds for the number of modes of two-component mixtures of t distributions in any dimension. In case of proportional dispersion matrices, these have at most three modes, while for equal degrees of freedom and equal dispersion matrices, the number of modes is at most two. We also give numerical illustrations and indicate applications to clustering and hypothesis testing.

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A likelihood ratio test for bimodality in two-component mixtures with application to regional income distribution in the EU

Abstract: Bimodality, Convergence analysis, Cross-sectional income distribution, Likelihood ratio test, Finite mixture,

Cited by 47 publications

References 25 publications

Distribution dynamics of regional GDP per employee in unified Germany

Distribution dynamics of regional GDP per employee in unified Germany

Historical Ethnic Homelands and Income Convergence in Africa

On the Number of Modes of Finite Mixtures of Elliptical Distributions

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