Pretest Estimator for Individual Normal Means with Meta-analytic Data

• Published in: Journal of the Japan Statistical Society, Japanese Issue Vol. 54; no. 2; pp. 73 - 108
• Main Authors: Emura, Takeshi, Chang, Yuan-Tsung, Taketomi, Nanami, Konno, Yoshihiko, Mori, Mihoko
• Format: Journal Article
• Language: Japanese
• Published: Japan Statistical Society 04.03.2025; 一般社団法人 日本統計学会
• Subjects: General Pretest推定量; Pretest推定量; メタ分析; 正規分布; 縮小推定量
• ISSN: 0389-5602; 2189-1478
• DOI: 10.11329/jjssj.54.73

Meta-analysis is a statistical method to summarize quantitative results from a set of published studies. Meta-analysis often assumes that the outcomes of all individual studies have a common mean and estimates the common mean based on the results of each study. On the other hand, meta-analysis sometimes shows an updated estimate of individual study. This paper is a review article for estimation of individual normal means based on pretest estimators using meta-analytic data. New results on the bias, mean squared error, and variance of the pretest estimator are also included in this paper. The use of the R package: meta.shrinkage is also described. An example of the application to eye allergic reaction data during anatomy practice is also reported.