Confidence bands for the difference of two quantile residual life functions with right censored data

Abstract

Quantile residual life function is widely used in many fields such as reliability and medical studies For right censored data Tsai (2015) used Wald type stochastic process to construct confidence band for a quantile residual life function Because the distribution of the supremum of the asymptotic process of Wald type stochastic process cannot be obtained analytically so Tsai (2015) used bootstrap method to obtain the critical point to construct confidence band For complete data Franco-Pereira et al (2012) used statistical depth to construct confidence band for the difference of two quantile residual life functions Similarly they used bootstrap method to obtain the critical point in order to construct confidence bands However right censored data are collected in many medical studies Therefore this thesis constructs confidence band for the difference of two quantile residual life functions for right censored data A Wald type stochastic process based on the two sample quantile residual life functions is used to construct confidence bands Likewise the distribution of the supremum of the asymptotic process of the Wald type stochastic process cannot be obtained analytically so the bootstrap method is used to obtain the critical point In addition the method used by Parzen et al (1997) is generalized to obtain the critical point in order to establish confidence band The simulation study shows that the coverage rate of the confidence band which critical point obtained by bootstrap method is close to the nominal coverage rate for large sample size

Date of Award	2019
Original language	English
Supervisor	Yun-Chan Chi (Supervisor)