Calibrated estimators using non-linear calibration constraints

ABSTRACT

In this paper, the problem of estimation of mean through calibration technique has been discussed. In the current investigation, we proposed new calibrated estimators of mean in simple random sampling, probability proportional to size sampling and stratified random sampling by considering non-linear constraints of an auxiliary variable. It has been shown through simulation study that the resultant estimators are more efficient than the combined regression as well as the combined ratio estimator in all three sampling designs.

KEYWORDS:

• Design weights
• calibrated weights
• Lagrangian multipliers
• simple random sampling
• probability proportional to size sampling
• stratified random sampling
• proportional allocation
• relative efficiency
• simulation study

Acknowledgements

The authors are thankful to the Editor in Chief: Dr Richard Krutchkoff for bringing this paper in the final form. This work was done by the lead author Shameem Alam while visiting the Department of Mathematics, Texas A$\mathrm{\&}$M University-Kingsville, Kingsville, TX with a scholarship (No:1-8/HEC/HRD/2018/8855) offered by the Higher Education Commission H-9 Islamabad, Pakistan.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Shameem Alam http://orcid.org/0000-0002-2926-4283

Sarjinder Singh http://orcid.org/0000-0002-3138-9640

Javid Shabbir http://orcid.org/0000-0002-0035-7072