Minimum variance stratification for scrambled response

Article type: Research Article

Authors: Verma, M.R.^{a; *} | Mahajan, P.K.^b | Dhall, S.P.^b

Affiliations: [a] Division of Agricultural Economics and Statistics, ICAR Research Complex for N.E.H. Region, Umiam (Barapani) Meghalaya Pin 793 103, India | [b] Department of Basic Sciences, University of Horticulture and Forestry, Nauni (Solan) Himachal Pradesh Pin 173230, India

Correspondence: [*] Corresponding author. Tel.: +91 364 2570635 (O); Fax: +91 364 2570363; E-mail: [email protected], [email protected]

Abstract: In this paper we have considered the problem of finding optimum strata boundaries (OSB) when the samples from different strata are selected with simple random sampling with replacement (SRSWR) and data are collected by scrambled randomized response technique on the sensitive variable. In the present paper a procedure which is applicable in more general situation is suggested for obtaining approximate optimum strata boundaries (AOSB). A limiting expression for the variance of the estimator of population mean, optimum number of strata, approximate expression for [nh] and expression for optimum cost allocated to L strata have also been suggested. The paper concludes with a numerical illustration.

Keywords: Optimum allocation, optimum stratification, AOSB, scrambled response, RRT

DOI: 10.3233/MAS-2006-1306

Journal: Model Assisted Statistics and Applications, vol. 1, no. 3, pp. 179-189, 2006