Annals of the Institute of Statistical Mathematics

, Volume 58, Issue 3, pp 457–473

Likelihood-based Inference for the Ratios of Regression Coefficients in Linear Models

  • Malay Ghosh
  • Gauri Sankar Datta
  • Dalho Kim
  • Trevor J. Sweeting

DOI: 10.1007/s10463-005-0027-3

Cite this article as:
Ghosh, M., Datta, G.S., Kim, D. et al. Ann Inst Stat Math (2006) 58: 457. doi:10.1007/s10463-005-0027-3


We consider the standard linear multiple regression model in which the parameter of interest is the ratio of two regression coefficients. Our setup includes a broad range of applications. We show that the 1− α confidence interval for the interest parameter based on the profile, conditional profile, modified profile or adjusted profile likelihood can potentially become the entire real line, while appropriately chosen integrated likelihoods do not suffer from this drawback. We further explore the asymptotic length of confidence intervals in order to compare integrated likelihood-based proposals. The analysis is facilitated by an orthogonal parameterization.


Adjusted profile likelihoodAdjustments to profile likelihoodConditional profile likelihoodExpected length of confidence intervalIntegrated likelihoodOrthogonal transformationProfile likelihood

Copyright information

© The Institute of Statistical Mathematics, Tokyo 2006

Authors and Affiliations

  • Malay Ghosh
    • 1
  • Gauri Sankar Datta
    • 2
  • Dalho Kim
    • 3
  • Trevor J. Sweeting
    • 4
  1. 1.Department of StatisticsUniversity of FloridaGainesvilleUSA
  2. 2.Department of StatisticsUniversity of GeorgiaAthensUSA
  3. 3.Department of StatisticsKyungpook National UniversityTaeguSouth Korea
  4. 4.Department of Statistical ScienceUniversity College LondonLondonUK