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Obtaining similar null distributions in the normal linear model using computational methods

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  • Klugkist, Irene
  • Hoijtink, Herbert

Abstract

Hypothesis testing when the null hypothesis belongs to the univariate or multivariate normal linear model is discussed. More specifically it is shown how data can be replicated from the null distribution conditional on the sufficient statistics for the parameters of the null hypothesis at hand. This distribution will be called the similar null distribution of the data. It is shown how the similar null distribution of the data can be used to obtain level alpha tests for any test statistic that is of interest. The p-value that is obtained using the distribution of the test statistic conditional on the sufficient statistics is called the similar p-value.

Suggested Citation

  • Klugkist, Irene & Hoijtink, Herbert, 2009. "Obtaining similar null distributions in the normal linear model using computational methods," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 877-888, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:877-888
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    References listed on IDEAS

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    1. Bayarri, M.J. & Castellanos, M.E. & Morales, J., 2006. "MCMC methods to approximate conditional predictive distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 621-640, November.
    2. Shoemaker L.H., 2003. "Fixing the F Test for Equal Variances," The American Statistician, American Statistical Association, vol. 57, pages 105-114, May.
    3. Singh, Parminder & Liu, Wei, 2006. "A test against an umbrella ordered alternative," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1957-1964, December.
    4. Tian, Guo-Liang & Ng, Kai Wang & Tan, Ming, 2008. "EM-type algorithms for computing restricted MLEs in multivariate normal distributions and multivariate t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4768-4778, June.
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