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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.

An optimal purely sequential strategy with asymptotic second-order properties: Applications from statistical inference and data analysis