Abstract: We add a log-concave qualitative constraint on the baseline distribution of the proportional odds model. A full maximum likelihood method is developed for the joint estimation of the regression parameters and densities. The asymptotic properties of the estimates are established. A likelihood ratio test is constructed to test the significance of the regression parameter. We also propose a Kolmogorov-Smirnov type test to assess the log-concavity of the baseline distribution. A simulation study and an application to data from the Chicago Healthy Aging Study show the usefulness of our method.

Key words and phrases: Density ratio model, exponential tilting, semiparametric method, shape constrained estimation, survival analysis.