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Adjustment of the Profile Likelihood for a Class of Normal Regression Models

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  • Maria Durban
  • I. D. Currie

Abstract

We apply the method of McCullagh & Tibshirani (1990) to a generalization of the model for variance components in which the parameter of interest can appear in both the mean and variance. We obtain the exact adjusted profile log‐likelihood score function. For the variance components model, we obtain the adjusted profile log‐likelihood and show that it equals the restricted log‐likelihood of Patterson & Thompson (1971). We discuss an example due to Kempton (1982) of a regression model with autoregressive terms in which the parameter of interest appears in both the mean and variance.

Suggested Citation

  • Maria Durban & I. D. Currie, 2000. "Adjustment of the Profile Likelihood for a Class of Normal Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 535-542, September.
    • Handle: RePEc:bla:scjsta:v:27:y:2000:i:3:p:535-542
    DOI: 10.1111/1467-9469.00205
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    Cited by:

    1. Federico Martellosio & Grant Hillier, 2019. "Adjusted QMLE for the spatial autoregressive parameter," Papers 1909.08141, arXiv.org.
    2. Yu, Dalei & Bai, Peng & Ding, Chang, 2015. "Adjusted quasi-maximum likelihood estimator for mixed regressive, spatial autoregressive model and its small sample bias," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 116-135.
    3. Céline Cunen & Nils Lid Hjort, 2022. "Combining information across diverse sources: The II‐CC‐FF paradigm," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 625-656, June.
    4. Guolo, Annamaria & Brazzale, Alessandra R. & Salvan, Alessandra, 2006. "Improved inference on a scalar fixed effect of interest in nonlinear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1602-1613, December.
    5. Martellosio, Federico & Hillier, Grant, 2020. "Adjusted QMLE for the spatial autoregressive parameter," Journal of Econometrics, Elsevier, vol. 219(2), pages 488-506.

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