Bayesian bounds for population proportion under ranked set sampling. Issue 2 (7th February 2019)

• Record Type: Journal Article
• Authors: Verma, Vivek; Nath, Dilip C.; Das, Radhakanta
• Is Part Of: Communications in statistics. Volume 48:Issue 2(2019)
• Page Start: 478
• Page End: 493
• Publication Date: 2019-02-07
• Subjects: Bayesian Cramer Rao bound -- Cramer Rao bound -- Fisher information -- Ranked set sampling; Primary 62F -- Secondary 62F10, 62F15; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2017.1387659
• Languages: English
• ISSNs: 0361-0918

Abstract

ABSTRACT: In this article, we consider a dichotomous population characterized by the parameter p defined as the proportion of individuals in the population possessing certain characteristic. The unknown proportion p is our parameter of interest in the present work. Under the assumption that p is a random quantity we derive a Bayesian Crammer–Rao (BCR) bound in connection with the estimation of p . The proposed procedure is based on a ranked set sample (RSS) observed on the variable of interest which is binary in nature. This RSS-based approach is compared with its corresponding SRS (simple random sample) counterpart in the cases of both perfect and imperfect rankings. The proposed procedure is applied for estimating the proportion of children aged12 -- 23 months (to the mothers aged 15–49 years of rural India) who are not immunized with the vaccine against measles using National Family Health Survey-3 (2005–2006) data of India.