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Date:
17 Jun 2006
Likelihoodbased Inference for the Ratios of Regression Coefficients in Linear Models
 Malay Ghosh,
 Gauri Sankar Datta,
 Dalho Kim,
 Trevor J. Sweeting
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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 likelihoodbased proposals. The analysis is facilitated by an orthogonal parameterization.
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 Title
 Likelihoodbased Inference for the Ratios of Regression Coefficients in Linear Models
 Journal

Annals of the Institute of Statistical Mathematics
Volume 58, Issue 3 , pp 457473
 Cover Date
 20060901
 DOI
 10.1007/s1046300500273
 Print ISSN
 00203157
 Online ISSN
 15729052
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Adjusted profile likelihood
 Adjustments to profile likelihood
 Conditional profile likelihood
 Expected length of confidence interval
 Integrated likelihood
 Orthogonal transformation
 Profile likelihood
 Industry Sectors
 Authors

 Malay Ghosh ^{(1)}
 Gauri Sankar Datta ^{(2)}
 Dalho Kim ^{(3)}
 Trevor J. Sweeting ^{(4)}
 Author Affiliations

 1. Department of Statistics, University of Florida, Gainesville, FL, 32611, USA
 2. Department of Statistics, University of Georgia, Athens, GA, 30602, USA
 3. Department of Statistics, Kyungpook National University, Taegu, South Korea
 4. Department of Statistical Science, University College London, WC1E 6BT, London, UK