An optimal purely sequential strategy with asymptotic second-order properties: Applications from statistical inference and data analysis. Issue 3 (30th September 2022)

• Record Type: Journal Article
• Authors: Bishnoi, Srawan Kumar; Mukhopadhyay, Nitis
• Is Part Of: Sequential analysis. Volume 41:Issue 3(2022)
• Page Start: 325
• Page End: 366
• Publication Date: 2022-09-30
• Subjects: Asymptotics -- exponential scale -- first-order properties -- fixed-size confidence region (FSCR) -- fixed-width confidence interval (FWCI) -- minimum risk point estimation (MRPE) -- multiple comparisons -- negative exponential location -- normal means -- optimal strategy -- scale family -- second-order properties -- selection and ranking; 62L10 -- 62L05 -- 62L12 -- 62F25; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2022.2096900
• Languages: English
• ISSNs: 0747-4946

Abstract

Abstract: We develop a new class of purely sequential methodologies under an assumption that the population distribution belongs to a location-scale family. Both asymptotic first-order and second-order theories are put forward with substantial generality under a big and unified tent that successfully lead to a broad set of illustrations. After we identify an appropriately defined optimal strategy under this unified structure, we introduce applications that handle a variety of interesting inference problems. These are associated with, but not limited to, the following areas: (a) the fixed-width confidence interval (FWCI) estimation, (b) the minimum risk point estimation (MRPE), (c) the fixed-size confidence region (FSCR) estimation, (d) multiple comparisons, and (e) selecting the best normal treatment (StBNT). In illustrations (a)–(d), we have highlighted a number of choices of population distributions. Some illustrations are accompanied with data analyses.