Some variants of adaptive sampling procedures and their applications

Abstract

Sequential analysis as a sampling technique facilitates efficient statistical inference by considering less number of observations in comparison to the fixed sampling method. The optimal stopping rule dictates the sample size and also the statistical inference deduced thereafter. In this research we propose three variants of the already existing multistage sampling procedures and name them as (i) Jump and Crawl (JC), (ii) Batch Crawl and Jump (BCJ) and (iii) Batch Jump and Crawl (BJC) sequential sampling methods. We use the (i) normal, (ii) exponential, (iii) gamma and (iv) extreme value distributions for the point estimation problems under bounded risk conditions. We highlight the efficacy of using the right adaptive sampling plan for the bounded risk problems for these four distributions, considering two different loss functions, namely (i) squared error loss (SEL) and (ii) linear exponential (LINEX) loss functions. Comparison and analysis of our proposed methods with existing sequential sampling techniques is undertaken and the importance of this study is highlighted using extensive theoretical simulation runs.