Abstract
Estimation of the common mean of inverse Gaussian distributions with different scale-like parameters is considered. We study finite sample properties, second-order admissibility and Pitman closeness properties of the Graybill–Deal estimator of the common mean. The best asymptotically normal estimator of the common mean is derived when the coefficients of variations are known. When the scale-like parameters are unknown but ordered, an improved estimator of the common mean is proposed. We also derive estimators of the common mean using the modified profile likelihood method. A simulation study has been performed to compare among the estimators.
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The authors express sincere gratitude to the Reviewers, Associate Editor, and Editor in Chief for their constructive comments, which substantially improved the original manuscript.
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Bera, S., Jana, N. On estimating common mean of several inverse Gaussian distributions. Metrika 85, 115–139 (2022). https://doi.org/10.1007/s00184-021-00829-y
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DOI: https://doi.org/10.1007/s00184-021-00829-y
Keywords
- Graybill–Deal estimator
- Second-order admissible
- Pitman nearness
- Coefficient of variation
- Common mean
- Profile likelihood