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Practical Testing for Normal Mixtures

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  • Jin Seo Cho

    (Yonsei University)

Abstract

The current study provides the Gaussian versions used to test for normal mixtures. These versions are highly practical as they can directly be used to simulate the asymptotic critical values of standard tests, for example the likelihood-ratio or Lagrange multiplier tests. We investigate testing for two normal mixtures: one having a single variance and two distinct means, and another having a single mean and two different variances. We derive the Gaussian versions for the two models by associating the score functions with the Hermite and generalized Laguerre polynomials, respectively. Additionally, we compare the performance of the likelihood-ratio and Lagrange multiplier tests using the asymptotic critical values.

Suggested Citation

  • Jin Seo Cho, 2025. "Practical Testing for Normal Mixtures," Working papers 2025rwp-248, Yonsei University, Yonsei Economics Research Institute.
  • Handle: RePEc:yon:wpaper:2025rwp-248
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    More about this item

    Keywords

    Gaussian version; LR test; LM test; Hermite polynomial; Generalized Laguerre polynomial.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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