THE ASYMPTOTIC EQUIVALENCE OF THE FISHER INFORMATION MATRICES FOR TYPE I AND TYPE II CENSORED DATA FROM LOCATION-SCALE FAMILIES

Abstract

Type I and Type II censored data arise frequently in controlled laboratory studies concerning time to a particular event (e.g., death of an animal or failure of a physical device). Log-location-scale distributions (e.g., Weibull, lognormal, and loglogistic) are commonly used to model the resulting data. Maximum likelihood (ML) is generally used to obtain parameter estimates when the data are censored. The Fisher information matrix can be used to obtain large-sample approximate variances and covariances of the ML estimates or to estimate these variances and covariances from data. The derivations of the Fisher information matrix proceed differently for Type I (time censoring) and Type II (failure censoring) because the number of failures is random in Type I censoring, but length of the data collection period is random in Type II censoring. Under regularity conditions (met with the above-mentioned log-location-scale distributions), we outline the different derivations and show that the Fisher information matrices for Type I and Type II censoring are asymptotically equivalent.

Keywords:

• Censoring
• Maximum likelihood
• Survival

ACKNOWLEDGMENTS

We thank professors H.A. David and V.N. Nair for very useful discussion, comments, and suggestions that greatly simplified the presentation in the paper.