The confidence interval of the cross-sectional distribution of durations

Tian and Dixon (2022) derived the variance of the estimator of cross-sectional distribution of durations (CSD). In this paper, we apply both Fieller's method and the Delta method to derive confidence interval of CSD using this variance formula. (CSD) is a new estimator derived by Dixon (2012). It can be applied in general Taylor model (GT E) by Dixon and Bihan (2012) and hospital waiting times by Dixon and Siciliani (2009). We use Monte Carlo simulations to evaluate the empirical size of Fieller's method and delta method among different sample sizes. The empirical results show that both Fieller's method and the delta method are valid in terms of estimating the confidence interval of CSD. Finally, we use both methods for real data set: the UK CPI micro-price data. Depending on the application, we see that both methods provide reasonable CIs for CSD estimators.