Estimating the common parameter of normal models with known coefficients of variation: a sensitivity study of asymptotically efficient estimators

Abstract

In this article, estimation of the common parameter θ, when data X ₁, …, X _n are independent observations where each X _i is normally distributed N (d _i θ, θ²) and coefficients of variation 1/d ₁, …, 1/d _n are known, is treated. Such a setup is motivated by problems arising in medical, biological, and chemical experiments. We consider maximum likelihood, linear unbiased minimum variance type, linear minimum mean square, Pitman-type, and Bayes estimators of θ. Our results generalize work of previous authors in several ways. First, consideration of known but different coefficients of variation allows more flexibility in designing experiments. Secondly, our treatment can be directly applied to the case of dependent data with known correlation structure. Further, using Monte Carlo simulations, we supplement asymptotic findings with small-sample results. We also investigate the sensitivity of the estimators under various model misspecification scenarios.

Keywords:

• Curved normal family
• Premium-protection plot
• Sensitivity
• Simulations

Acknowledgements

We are very appreciative of valuable insights and comments provided by an anonymous referee, leading to many improvements in the article.