Nonparametric Estimation of Reliability and Related Functions

This project deals with several nonparametric inference problems including two-sample tests, linear regression and estimation of distribution and related functions such as density and hazard rate functions. Estimators with desired aging properties were constructed for IFRA and NBU distribution functions respectively based on randomly censored data and shown to be raised to the one half power equivalent to the product-limit estimator. Nonparametric maximum likelihood estimator and its strong consistency were also derived for an IFR distribution for unidentifiable cause-of-failure data. Local asymptotic properties strong consistency, asymptotic normality and mean squared error of the kernel density and hazard rate estimators were obtained via a recent i.i.d. representation of the product-limit estimator. The results on kernel estimates were applied to obtain point and interval estimates of the change-point of a hazard rate function. Several median type two-sample test procedures which allows early termination of the study were constructed. kr