Two-stage estimation for a normal mean having a known lower bound of variance with final sample size defined via Gini's mean difference and mean absolute deviation. Issue 2 (3rd April 2018)

• Record Type: Journal Article
• Authors: Mukhopadhyay, Nitis; Hu, Jun
• Is Part Of: Sequential analysis. Volume 37:Issue 2(2018)
• Page Start: 204
• Page End: 221
• Publication Date: 2018-04-03
• Subjects: Asymptotic first-order properties -- asymptotic second-order properties -- Gini's mean difference -- marigold data -- mean absolute deviation -- sample standard deviation -- simulations; 62L10 -- 62L05 -- 62L12 -- 62F25; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2018.1466532
• Languages: English
• ISSNs: 0747-4946

Abstract

Abstract: Revisiting Stein (1945, 1949 ) as well as Mukhopadhyay and Duggan (1997 ), we have proposed new two-stage procedures under both minimum risk point estimation and fixed-width confidence interval configurations for a normal mean μ when a lower bound of variance is known to us. New unbiased estimators based on sample standard deviation, Gini's mean difference (GMD), and mean absolute deviance (MAD) are constructed to define the final sample sizes. The new procedures enjoy both asymptotic first-order and second-order properties, followed by simulated performances. Real data illustrations of the marigold data are also included.