Abstract: We propose a new method for pointwise estimation of monotone, unimodal and U-shaped failure rates, under a right-censoring mechanism, using nonparametric likelihood ratios. The asymptotic distribution of the likelihood ratio is pivotal, though non-standard, and can therefore be used to construct asymptotic confidence intervals for the failure rate at a point of interest, via inversion. Major advantages of the new method lie in the facts that it completely avoids estimation of nuisance parameters, or the choice of a bandwidth/tuning parameter, and is extremely easy to implement. The new method is shown to perform competitively in simulations, and is illustrated on a data set involving time to diagnosis of schizophrenia in the Jerusalem Perinatal Cohort Schizophrenia Study.
Key words and phrases: Asymptotic pivots, greatest convex minorant, likelihood ratio statistic, monotone hazard rate, two-sided Brownian motion, universal limit.