Estimation of a common mean of two normal distributions
The author considers the problem of estimating the common mean of two normal distributions with independent estimators for variances. The model for this purpose is that of \textit{C. G. Bhattacharya}, Ann. Stat. 8, 205- 211 (1980; Zbl 0422.62025). Through a set of four theorems, all of which are stated and proved in detail, the author gives sufficient conditions for the combined estimator to be better than the un-combined estimator, in the sense that its variance is smaller. These results are applied to two situations. The first one is the problem of recovery of interblock information in balanced incomplete block designs (BIBD). The second application is to the problem of estimating common regression coefficients of two normal linear models. In these applications, again, two more theorems are proved, one for each application. In this connection, attention is brought to the works of \textit{L. D. Brown} and \textit{A. Cohen}, Ann. Stat. 2, 963-976 (1974; Zbl 0305.62019) and of \textit{C. G. Khatri} and \textit{K. R. Shah}, Commun. Stat. 3, 647-663 (1974; Zbl 0299.62021).
estimating the common mean of two normal distributions
estimating common regression coefficients of two normal linear models
scientific article; zbMATH DE number 4041046