Journal of the Iranian Statistical Society

Two-Step Calibration Estimator with Double Use of Auxiliary Variable: Method and Application

Document Type : Original Article

Authors

1 Department of Mathematics and Statistics, Banasthali University, Rajasthan, 304022, India

2 Department of Statistics, Banaras Hindu University, UP, 221005, India.

3 Department of Economics, Finance and Statistics, Jonkoping University, Jonkoping, 55111, Sweden.

Abstract

This article introduces a two-step calibration technique for the inverse relationship between study variable and auxiliary variable along with the double use of the auxiliary variable. In the first step, the calibration weights and design weights are set proportional to each other for a given sample. While in the second step, the constant of proportionality is to be obtained on the basis of some different objectives of the investigation viz. bias reduction or minimum Mean Squared Error (MSE) of the proposed estimator. Many estimators based on inverse relationship between $x$ and $y$ have been already developed and are considered to be special cases of the proposed estimator. Properties of the proposed estimator is discussed in details. Moreover, a simulation study has also been conducted to compare the performance of the proposed estimator under Simple Random Sampling Without Replacement (SRSWOR) and Lahiri-Midzuno (L-M) sampling design in terms of percent relative bias and MSE. The benefits of two-step calibration estimator are also demonstrated using real life data.

Keywords

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Journal of the Iranian Statistical Society
Volume 21, Issue 1
June 2022
Pages 37-54
  • Receive Date: 01 August 2020
  • Revise Date: 07 August 2022
  • Accept Date: 21 December 2022