Bias corrected maximum likelihood estimators under progressive type-I interval censoring scheme

In survival analysis naturally observed lifetimes are not of large size and so the most commonly used maximum likelihood (ML) estimator that is often biased needs to be corrected in the sense of bias. In this paper, exact expression for the Fisher Information matrix under progressive type-I interval censoring (PTIC) scheme is given. Using the method proposed by Cox and Snell (J. Royal Stat. Soc. B., 30:248-265, 1968), we construct the first-order bias corrected maximum likelihood (BML) estimator under PTIC scheme. As an application, performance of the ML and BML estimators are compared by simulations when generated realizations under PTIC scheme follow Chen distribution. Furthermore, performance of the BML estimator is demonstrated through three sets of real data.