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Inference for a skew extension of the Grubbs model

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Abstract

In this paper, we discuss inferential aspects for the Grubbs model when the unknown quantity x (latent response) follows a skew-normal distribution, extending early results given in Arellano-Valle et al. (J Multivar Anal 96:265–281, 2005b). Maximum likelihood parameter estimates are computed via the EM-algorithm. Wald and likelihood ratio type statistics are used for hypothesis testing and we explain the apparent failure of the Wald statistics in detecting skewness via the profile likelihood function. The results and methods developed in this paper are illustrated with a numerical example.

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Authors and Affiliations

  1. Departamento de Estatística, Universidade Federal de Minas Gerais, Av. Antonio Carlos 6627, Belo Horizonte, MG, CEP 31270-901, Brazil

    Lourdes C. Montenegro

  2. Departamento de Estatística, Universidade Estadual de Campinas, Caixa Postal 6065, Campinas, SP, CEP 13083-970, Brazil

    Víctor H. Lachos

  3. Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, São Paulo, SP, CEP 05311-970, Brazil

    Heleno Bolfarine

Authors
  1. Lourdes C. Montenegro
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  2. Víctor H. Lachos
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  3. Heleno Bolfarine
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Corresponding author

Correspondence to Víctor H. Lachos.

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Montenegro, L.C., Lachos, V.H. & Bolfarine, H. Inference for a skew extension of the Grubbs model. Stat Papers 51, 701–715 (2010). https://doi.org/10.1007/s00362-008-0157-9

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  • DOI: https://doi.org/10.1007/s00362-008-0157-9

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