End-Point Estimation for Decreasing Densities: Asymptotic Behaviour of the Penalized Likelihood Ratio

We consider the problem of estimating the modal value of a decreasing density on the positive real line. This has application in several interesting phenomena arising, for example, in renewal theory, and in biased and distance samplings. We use a penalized likelihood ratio-based approach for inference and derive the scale-free universal large sample null distribution of the log-likelihood ratio, using a suitably chosen penalty parameter. We present simulation results and a real data analysis to corroborate our findings, and compare the performance of the confidence sets with the existing results. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.