Unbiased estimator for a covariance matrix in a three-step monotone incomplete sample

Abstract In a monotone incomplete sample, the maximum likelihood estimator (MLE) for a mean vector is unbiased, whereas the MLE for a covariance matrix is not. This study derives unbiased estimators (UBEs) for a covariance matrix in a three-step monotone incomplete sample. We further investigate the properties of the estimators, compare risks of the estimators and the MLE, and check accuracies through numerical simulation.