Shrinkage estimation for the rate parameter under the exponential distribution with censored survival data

The exponential distribution is widely applied in survival and reliability analyses. To estimate the rate parameter of the exponential distribution with censored survival data, maximum likelihood estimation is usually employed. However, in case the number of events or subjects is small for the data, the maximum likelihood estimator can have large bias and variance. In this article, we propose a shrinkage estimator for the rate parameter of the exponential distribution using a penalized log-likelihood by adding a penalty for a large parameter value. We also derive theoretical properties of the penalized maximum likelihood estimator. Simulation results show that the proposed method provides a smaller mean squared error than the maximum likelihood estimation. Finally, we apply the proposed method to the practical data.