The variances of non-parametric estimates of the cross-sectional distribution of durations

Abstract This paper focuses on the link between non-parametric survival analysis and three distributions. The delta method is applied to derive the variances of the non-parametric estimators of three distributions: the distribution of durations (DD), the cross-sectional distribution of ages (CSA) and the cross-sectional distribution of (completed) durations (CSD). The non-parametric estimator of the the cross-sectional distribution of durations (CSD) has been defined and derived by Dixon (2012) and used in the generalized Taylor price model (GTE) by Dixon and Le Bihan (2012). The Monte Carlo method is applied to evaluate the variances of the estimators of DD and CSD and how their performance varies with sample size and the censoring of data. We apply those estimators to two data sets: the UK CPI micro-price data and waiting-time data from UK hospitals. Both the estimates of the distributions and their variances are calculated. Depending on the empirical results, the estimated variances indicate that the DD and CSD estimators are all significant.