Minimum risk point estimation for a function of a normal mean under weighted power absolute error loss plus cost: First-order and second-order asymptotics. Issue 3 (3rd July 2021)

• Record Type: Journal Article
• Authors: Banerjee, Soumik; Mukhopadhyay, Nitis
• Is Part Of: Sequential analysis. Volume 40:Issue 3(2021)
• Page Start: 336
• Page End: 369
• Publication Date: 2021-07-03
• Subjects: Accelerated sequential sampling -- first-order properties -- minimum risk -- nonlinear cost -- nonlinear renewal theory -- power error absolute loss -- purely sequential sampling -- regret -- risk efficiency -- second-order properties -- simulations -- three-stage sampling; 62L12 -- 62L10 -- 62L05; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2021.1940496
• Languages: English
• ISSNs: 0747-4946

Abstract

Abstract: We have designed multistage minimum risk point estimation (MRPE) strategies for a function of an unknown mean in a normal population with its variance unknown. These are developed under a weighted power absolute error loss (PAEL) function plus nonlinear cost of sampling by incorporating purely sequential, accelerated sequential, and three-stage estimation methodologies. Crucial asymptotic first-order and asymptotic second-order properties have been proved thoroughly under all three MRPE strategies. Extensive sets of simulations tend to validate nearly all desirable asymptotic properties for small to medium to large optimal fixed sample sizes.