Comparing two treatments in terms of the likelihood ratio order Articles uri icon

authors

  • MARTIN APAOLAZA, NIRIAN
  • Mata, Raquel
  • PARDO, LEANDRO

publication date

  • January 2015

start page

  • 3512

end page

  • 3534

issue

  • 17

volume

  • 85

international standard serial number (ISSN)

  • 0094-9655

electronic international standard serial number (EISSN)

  • 1563-5163

abstract

  • In this paper new families of test-statistics are introduced and studied for the problem of comparing two treatments in terms of the likelihood ratio order. The considered families are based on phi-divergence measures and arise as natural extensions of the classical likelihood ratio test and Pearson test-statistics. It is proven that their asymptotic distribution is a common chi-bar random variable. An illustrative example is presented and the performance of these statistics is analysed through a simulation study. Through a simulation study it is shown that, for most of the proposed scenarios adjusted to be small or moderate, some members of this new family of test-statistic display clearly better performance with respect to the power in comparison to the classical likelihood ratio and the Pearson's chi-square test while the exact size remains closed to the nominal size. In view of the exact powers and significance levels, the study also shows that the Wilcoxon test-statistic is not as good as the two classical test-statistics.

keywords

  • divergence measure; kullback divergence measure; inequality constrains; likelihood ratio-order; loglinear models; log-linear models; constraints; statistics; estimators; inference