Estimation with left-truncated and right censored data: A comparison study

Estimation based on the left-truncated and right randomly censored data arising from a general family of distributions is considered. In the special case, when the random variables satisfy a proportional hazard model, the maximum likelihood estimators (MLEs) as well as the uniformly minimum variance unbiased estimators (UMVUEs) of the unknown parameters are obtained. Explicit expressions for the MLEs are obtained when the random variables follow an exponential distribution. In the latter case, three different estimators for the parameter of interest are proposed. These estimators are compared using the criteria of mean squared error (MSE) and Pitman measure of closeness (PMC). It is shown that shrinking does not always yield a better estimator.