Likelihood Inference: Type-I and Type-II Censoring

In Chapter 6, we considered linear inference based on progressively Type-II censored order statistics. Linear inference is popular because, in addition to having many desirable properties which we associate with good estimators, linear estimators have a very simple form, viz, the estimators are linear combinations of observed data values. As a result, these estimators are often quite simple to interpret from a practitioner’s point of view. Furthermore, we are able to very easily calculate the variances and covariance of linear estimators. This is not always true for other types of estimators, such as maximum likelihood and moment estimators. However, the linear inference that we have discussed applies only to scale- or location-scale families of distributions. If a new parameter, such as a shape parameter or a threshold parameter that can not be written as a simple shift from the standard distribution, is introduced, other methods of estimating these parameters need to be considered.