Handling non-response in the presence of extreme values

Articles in Press

Document Type : Original Article

Authors
Syed Abdul Rehman 1
Shabbir Javid 2
1 Department of Mathematical Sciences, BUITEMS, Pakistan
2 Department of Statistics, Unoversity of Wah, Wah, Pakistan
10.22034/jirss.2026.1999131.1006
Abstract
Non-response and extreme values are two major issues faced by surveyors at the survey and estimation stage; they lead to biased and inefficient estimators. This study proposes four unbiased estimators of the finite population mean in the presence of extreme values when non-response occurs in surveys. We consider two robust ranked set sampling (RSS) designs, called improved paired RSS (IPRSS) and median RSS (MRSS) for the derivation of the proposed estimators. Expressions are provided for the variance of the proposed estimator, and it is mathematically proved that these estimators are more efficient than the Hansen naïve model. Additionally, the efficiency conditions are provided in comparison with the Bouza model of handling non-response in RSS. We conduct a comprehensive simulation study to observe the relative efficiency of the proposed estimators based on hypothetical normal data. For applications in real life, we also consider heart failure data for simulations.
Keywords
Extreme value theory
concomitant variable
order statistics
Monte Carlo simulation
relative efficiency
Subjects
Abu-Dayyeh WA, Ahmed MS, Ahmed RA, Muttlak HA. Some estimators of a finite population mean using auxiliary information. Applied Mathematics and Computation. 2003;139(2–3):287–298.
Al-Saleh MF, Al-Kadiri MA. Double-ranked set sampling. Statistics and Probability Letters. 2000;48(2):205–212.
Bouza-Herrera CN. Handling Missing Data in Ranked Set Sampling. Springer; 2013.
Fatima M, Shahbaz SH, Hanif M, Shahbaz MQ. A modified regression-cum-ratio estimator for finite population mean in presence of nonresponse using ranked set sampling. AIMS Mathematics. 2022;7(4):6478–6488.
Hansen MH, Hurwitz WN. The problem of non-response in sample surveys. Journal of the American Statistical Association. 1946;41(236):517–529.
Haq A, Brown J, Moltchanova E, Al-Omari AI. Paired double-ranked set sampling. Communications in Statistics - Theory and Methods. 2016;45(10):2873–2889.
Kadilar C, Cingi H. A new estimator using two auxiliary variables. Applied Mathematics and Computation. 2005;162(2):901–908.
Malik S, Singh R. An improved estimator using two auxiliary attributes. Applied Mathematics and Computation. 2013;219(23):10983–10986.
McIntyre GA. A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research. 1952;3(4):385–390.
Muneer S, Shabbir J, Khalil A. Estimation of finite population mean in simple random sampling and stratified random sampling using two auxiliary variables. Communications in Statistics - Theory and Methods. 2017;46(5):2181–2192.
Muttlak HA. Median ranked set sampling with concomitant variables and a comparison with ranked set sampling and regression estimators. Environmetrics. 1998;9(3):255–267.
Rehman SA, Shabbir J. On the improvement of paired ranked set sampling to estimate population mean. Statistics in Transition New Series. 2021;22(3):145–161.
Samawi HM, Tawalbeh EM. Double median ranked set sample: Comparing to other double ranked samples for mean and ratio estimators. Journal of Modern Applied Statistical Methods. 2002;1(2):428–438.
Singh HP, Tailor R, Singh S. General procedure for estimating the population mean using ranked set sampling. Journal of Statistical Computation and Simulation. 2014;84(5):931–945.
Singh R, Sharma P. A class of exponential ratio estimators of finite population mean using two auxiliary variables. Pakistan Journal of Statistics and Operation Research. 2015;11(2):221–229.
Stokes SL. Ranked set sampling with concomitant variables. Communications in Statistics - Theory and Methods. 1977;6(12):1207–1211.
Takahasi K, Wakimoto K. On unbiased estimates of the population mean based on the sample stratified by means of ordering. Annals of the Institute of Statistical Mathematics. 1968;20(1):1–31.
Journal of the Iranian Statistical Society

Articles in Press, Accepted Manuscript
Available Online from 20 July 2026

  • Receive Date 28 March 2023
  • Revise Date 11 July 2026
  • Accept Date 11 July 2026