Exact inference for the difference of Laplace location parameters

Maria Tafiadi and George Iliopoulos ()
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Maria Tafiadi: University of Piraeus
George Iliopoulos: University of Piraeus

Metrika: International Journal for Theoretical and Applied Statistics, 2017, vol. 80, issue 6, No 13, 829-861

Abstract: Abstract We consider exact procedures for testing the equality of means (location parameters) of two Laplace populations with equal scale parameters based on corresponding independent random samples. The test statistics are based on either the maximum likelihood estimators or the best linear unbiased estimators of the Laplace parameters. By conditioning on certain quantities we manage to express their exact distributions as mixtures of ratios of linear combinations of standard exponential random variables. This allows us to find their exact quantiles and tabulate them for several sample sizes. The powers of the tests are compared either numerically or by simulation. Exact confidence intervals for the difference of the means corresponding to those tests are also constructed. The exact procedures are illustrated via a real data example.

Keywords: Laplace (double exponential) distribution; Difference of means; Exact tests; Exact confidence intervals; Maximum likelihood estimators; Best linear unbiased estimators; Ratios of linear combinations of exponential random variables (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00184-017-0630-3

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