Minimum-Distance Parametric Estimation Under Progressive Type-I Censoring

The objective of this paper is to provide a new estimation method for parametric models under progressive Type-I censoring. First, we propose a Kaplan-Meier nonparametric estimator of the reliability function taken at the censoring times. It is based on the observable number of failures, and the number of censored units occurring from the progressive censoring scheme at the censoring times. This estimator is then shown to asymptotically follow a normal distribution. Next, we propose a minimum-distance method to estimate the unknown Euclidean parameter of a given parametric model. This method leads to consistent, asymptotically normal estimators. The maximum likelihood estimation method based on group-censored samples is discussed next, and the efficiencies of these two methods are compared numerically. Then, based on the established results, we derive a method to obtain the optimal Type-I progressive censoring scheme, Finally we illustrate all these results through a Monte Carlo simulation study, and an illustrative example.