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A Simple Identification Proof for a Mixture of Two Univariate Normal Distributions

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Abstract

A simple proof of the identification of a mixture of two univariate normal distributions is given. The proof is based on the equivalence of local identification with positive definiteness of the information matrix and the equivalence of the latter to a condition on the score vector that is easily checked for this model. Two extensions using the same line of proof are also given.

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Authors and Affiliations

  1. RAND Corporation and University of Groningen, Santa Monica, USA

    Erik Meijer

  2. University College London and University of Groningen, Santa Monica, USA

    Jelmer Y. Ypma

  3. RAND Corporation, 1776 Main St, PO Box 2138, Santa Monica, CA, 90407-2138, USA

    Erik Meijer

Authors
  1. Erik Meijer
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  2. Jelmer Y. Ypma
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Correspondence to Erik Meijer.

Additional information

We would like to thank Tom Wansbeek, Michel Wedel, Arie Kapteyn, and two anonymous reviewers for helpful comments on earlier versions of this paper.

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Meijer, E., Ypma, J.Y. A Simple Identification Proof for a Mixture of Two Univariate Normal Distributions. J Classif 25, 113–123 (2008). https://doi.org/10.1007/s00357-008-9008-6

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  • DOI: https://doi.org/10.1007/s00357-008-9008-6

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