An Efficient Class of Calibration Ratio Estimators of Domain Mean in Survey Sampling
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An Efficient Class of Calibration Ratio Estimators of Domain Mean in Survey Sampling Ekaette I. Enang1 · Etebong P. Clement2 Received: 8 July 2017 / Revised: 16 November 2018 / Accepted: 27 December 2018 © School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract This paper develops a new approach to domain estimation and proposes a new class of ratio estimators that is more efficient than the regression estimator and not depending on any optimality condition using the principle of calibration weightings. Some wellknown regression and ratio-type estimators are obtained and shown to be special members of the new class of estimators. Results of analytical study showed that the new class of estimators is superior in both efficiency and biasedness to all related existing estimators under review. The relative performances of the new class of estimators with a corresponding global estimator were evaluated through a simulation study. Analysis and evaluation are presented. Keywords Auxiliary variable · Calibration approach · Efficiency · Global estimator · Ratio-type estimator · Stratified sampling · Study variable Mathematics Subject Classification 62D05 · 62G05 · 62H12
1 Introduction It is well known that the ratio and product estimators most practically have the limitation of having efficiency not exceeding that of the regression estimator. In the progression for better ratio (or product) estimators, authors like Singh and Vishwakarma [22], Sharma and Tailor [19], Onyeka [16], Singh and Audu [23], and Clement [2–4] have provided modifications to the existing ratio and product estima-
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Etebong P. Clement [email protected] Ekaette I. Enang [email protected]
1
Department of Statistics, University of Calabar, Calabar, Nigeria
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Department of Mathematics and Statistics, University of Uyo, Uyo, Nigeria
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E. I. Enang, E. P. Clement
tors to provide better alternatives and improve their precision. However, it has been observed that though the proposed estimators are improvement over existing ones, their performances depend on some optimality conditions that need to be satisfied to guarantee better estimates. This paper introduces a new class of ratio estimators that is more efficient than the regression estimator and which does not depend on any optimality condition using the principle of calibration weightings. The concept of calibration estimation was introduced in survey sampling by Deville and Sarndal [9]. Calibration estimation has been studied by many survey statisticians. A few key references are Arnab and Singh [1], Kott [14], Sarndal [18], Kim et al. [12], Kim and Park [13], Rao et al. [17], Clement et al. [5] and Clement and Enang [6, 7].
2 The Proposed Class of Ratio Estimators Consider a finite population U of N elements U (U1 , U2 , . . . , U N ).
(2.1)
The finite population of Eq. (2.1) is divided into D domains U1 , U2 , . . . , U D of sizes N1 , N2 , . . . , N D , respectively. Consider stratified ra
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