Nonparametric tests for and against likelihood ratio ordering in the two-sample problem
1 Department of Mathematics, East Carolina University, Greenville, North Carolina 27858, U.S.A. carolanc{at}mail.ecu.edu, 2 Department of Statistics, Kansas State University, Manhattan, Kansas 66506, U.S.A. tebbs{at}ksu.edu
We derive nonparametric procedures for testing for and against likelihood ratio ordering in the two-population setting with continuous distributions. We account for this ordering by examining the least concave majorant of the ordinal dominance curve formed from the nonparametric maximum likelihood estimators of the continuous distribution functions F and G. In particular, we focus on testing equality of F and G versus likelihood ratio ordering and testing for a violation of likelihood ratio ordering. For both testing problems, we propose area-based and sup-norm-based test statistics, derive appropriate limiting distributions, and provide simulation results that characterise the performance of our procedures. We illustrate our methods using data from a controlled experiment involving the effects of radiation on mice.
Key Words: Isotonic regression; Kolmogorov–Smirnov; Least concave majorant; Local uniform ordering; Mann–Whitney; Order-restricted inference; Ordinal dominance curve; Stochastic ordering
Received July 2003. Revised June 2004.