Generalized robust-regression-type estimators under different ranked set sampling
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ORIGINAL RESEARCH
Generalized robust‑regression‑type estimators under different ranked set sampling Nursel Koyuncu1 · Amer Ibrahim Al‑Omari2 Received: 27 July 2020 / Accepted: 1 November 2020 © Islamic Azad University 2020
Abstract In this paper, we have proposed a new generalized robust estimators of population mean under different ranked set sampling. Robust estimators are recently defined by Zaman and Bulut (Commun Stat Theory Methods 48(8):2039–2048, 2019a) and Ali et al. (Commun Stat Theory Methods, 2019. https://doi.org/10.1080/03610926.2019.1645857) under simple random sampling. We have generalized robust-type estimators where Zaman and Bulut (2019a) and Ali et al. (2019) estimators are members of our generalized estimator. We have also extended our results to ranked set and median ranked set sampling designs. The simulation study showed that our proposed robust-type estimator performs better. Keywords Ratio-type estimators · Regression-type estimators · Robust regression methods · Ranked set sampling · Median ranked set sampling Mathematics Subject Classification 62D05 · 62F35
Introduction When the data set does not follow a normal distribution or contains outliers, estimations of parameters are affected badly. To overcome this difficulty and get reliable conclusions about the contaminated data, robust estimators are defined in statistical analysis. This relies on finding proper estimates of the data location and scale ([9, 10, 13]). Using information of auxiliary variable in the estimates also increases the efficiency. We can list some important studies as follows: Hanif and Shahzad [11] considered the issue of estimating the population variance utilizing trace of kernel matrix in absence of non-response under simple random sampling (SRS) scheme. Shahzad et al. [25] defined a new class of ratio-type estimators for the population mean.
* Nursel Koyuncu [email protected] Amer Ibrahim Al‑Omari [email protected] 1
Department of Statistics, Hacettepe University, Ankara, Turkey
Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq, Jordan
2
Shahzad et al. [26] proposed a new class of exponential-type estimators, based on the known median of study variable. The authors also studied robust ratio-type estimators when the data contained outliers. Zaman and Bulut [30] have studied the robust estimators in simple random sampling and they also extended their studies to stratified simple random sampling [31]. Recently, Ali et al. [1] generalized Zaman and Bulut [30]’s estimators and they have studied sensitive data case. Subzar et al. [28] adapted the various robust regression techniques to the ratio estimators. Shahzad et al. [27] defined class of regression-type estimators utilizing robust regression tools. Ranked set sampling (RSS) is an effective design introduced by [20]. The efficiency of RSS depends on the sampling allocation whether balanced or unbalanced. The balanced RSS features an equal allocation of the ranked order statistics. It has been shown theor
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