Nearest neighbor hazard estimation with left-truncated duration data

Duration data often suffer from both left-truncation and right-censoring. We show how both deficiencies can be overcome at the same time when estimating the hazard rate nonparametrically by kernel smoothing with the nearest-neighbor bandwidth. Smoothing Turnbull’s estimator of the cumulative hazard rate, we derive strong uniform consistency of the estimate from Hoeffding’s inequality, applied to a generalized empirical distribution function. We also apply our estimator to rating transitions of corporate loans in Germany.