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Estimation of regression vectors in linear mixed models with Dirichlet process random effects

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  • Chen Li
  • George Casella
  • Malay Ghosh

Abstract

The Dirichlet process has been used extensively in Bayesian non parametric modeling, and has proven to be very useful. In particular, mixed models with Dirichlet process random effects have been used in modeling many types of data and can often outperform their normal random effect counterparts. Here we examine the linear mixed model with Dirichlet process random effects from a classical view, and derive the best linear unbiased estimator (BLUE) of the fixed effects. We are also able to calculate the resulting covariance matrix and find that the covariance is directly related to the precision parameter of the Dirichlet process, giving a new interpretation of this parameter. We also characterize the relationship between the BLUE and the ordinary least-squares (OLS) estimator and show how confidence intervals can be approximated.

Suggested Citation

  • Chen Li & George Casella & Malay Ghosh, 2018. "Estimation of regression vectors in linear mixed models with Dirichlet process random effects," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(16), pages 3935-3954, August.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:16:p:3935-3954
    DOI: 10.1080/03610926.2017.1366519
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    Cited by:

    1. Ruochen Wu & Melvyn Weeks, 2020. "A Semi-Parametric Bayesian Generalized Least Squares Estimator," Papers 2011.10252, arXiv.org, revised Jan 2023.

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