Representation of Certain Covariance Matrices with Application to Asymptotic Efficiency

Abstract

Although maximum likelihood estimates are asymptotically efficient, they are often very hard to find. Replacement of some, but not all, of the equations in the maximum likelihood system may make it more manageable. The covariance matrices of the new estimator and of the estimating functions will have special structure in relation to the information matrix. These relationships are characterized and various properties that pertain to multiparameter efficiency are developed. Application is made to the estimation of parameters from the gamma distribution. Some new estimators are found and their efficiencies are compared.

Key Words:

• Covariance matrices
• Asymptotic efficiency
• Maximum likelihood modified
• Efficiency of equations