Hidekazu Tanaka, Nabendu Pal & Wooi K. Lim. On improved estimation of a gamma shape parameter. Statistics: A Journal of Theoretical and Applied Statistics. 2015;49:84–97. doi: 10.1080/02331888.2014.915842
After the above paper was submitted on 14th August 2013, and which was published online on the 10th June 2014, we came to know about a very similar paper by Takagi [Citation1]. Takagi derived a very general result giving conditions that are sufficient for proving second-order admissibility/inadmissibility of an estimator. On the other hand, we directly looked at three specific estimators of interest and checked their second-order optimality by using the theorem of Ghosh and Sinha [Citation2]. Therefore, second-order optimality of the three estimators can be seen from Takagi's Theorem 5.7 also. Further, we undertook a comprehensive simulation study of the three aforementioned estimators as well as their second-order improved versions.
Omission of Takagi's paper in our work is deeply regretted.
References
- Y Takagi. On the estimation of the shape parameter of the gamma distribution in second-order asymptotics. Statist Probab Lett. 2012;82:15–21. doi: 10.1016/j.spl.2011.09.002
- JK Ghosh, BK Sinha. A necessary and sufficient condition for second order admissibility with applications to Berkson's bioassay problem. Ann Statist. 1981;9:1334–1338. doi: 10.1214/aos/1176345650