Unbiased Estimator for a Covariance Matrix Under Two-Step Monotone Incomplete Sample

Abstract

In this article, we consider an inference for a covariance matrix under two-step monotone incomplete sample. The maximum likelihood estimator of the mean vector is unbiased but that of the covariance matrix is biased. We derive an unbiased estimator for the covariance matrix using some fundamental properties of the Wishart matrix. The properties of the estimators are investigated and the accuracies are checked by a numerical simulation.

Keywords:

• Covariance matrix
• Monotone incomplete sample
• Unbiasedness

Mathematics Subject Classification:

• Primary 62H12
• Secondary 62E20

Appendix A. Calculation of Asymptotic Covariance Matrix of the Estimator

In this section, we calculate the asymptotic covariance matrix for the MLE. Applying (10(10) ), (11(10) ), and (12(10) ), we obtain the asymptotic covariance matrices as follows: