Estimation of a common mean of two normal distributions
type: Item
instance of: scholarly article
title: Estimation of a common mean of two normal distributions
zbMATH Open document ID: 0638.62028
author: Tatsuya Kubokawa
published in: Tsukuba Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: 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).
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62K10
zbMATH DE Number: 4041046
zbMATH Keywords: estimating the common mean of two normal distributions
zbMATH Keywords: independent estimators for variances
zbMATH Keywords: sufficient conditions
zbMATH Keywords: combined estimator
zbMATH Keywords: un- combined estimator
zbMATH Keywords: recovery of interblock information
zbMATH Keywords: balanced incomplete block designs
zbMATH Keywords: estimating common regression coefficients of two normal linear models
reviewed by: G. S. Lingappaiah
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496160510
OpenAlex ID: W275486177
DOI: 10.21099/TKBJM/1496160510
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description: scientific article; zbMATH DE number 4041046