Stratified Ranked Set Sampling With Missing Observations for Estimating the Difference

Abstract

The authors develop the estimation of the difference of means of a pair of variables X and Y when we deal with missing observations. A seminal paper in this line is due to Bouza and Prabhu-Ajgaonkar when the sample and the subsamples are selected using simple random sampling. In this this chapter, the authors consider the use of ranked set-sampling for estimating the difference when we deal with a stratified population. The sample error is deduced. Numerical comparisons with the classic stratified model are developed using simulated and real data.

Inference for dependent complementary competing risks model from an inverted Kumaraswamy distribution under ranked set sampling

“…For better interpretation, the sketch of RSS process is described as follows: $$$$\begin{align*} \begin{matrix} \text{Set} & \text{Ranking} & & & & & \text{RSS} \\ 1 & \mathbf {X_{(1)1}} & X_{(2)1} & \cdots & X_{(n)1} & \longrightarrow & \mathbf {X_{(1)1}} \\ 2 & X_{(1)2} & \mathbf {X_{(2)2}} & \cdots & X_{(n)2} &\longrightarrow & \mathbf {X_{(2)2}} \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots \\ n & X_{(1)n} & X_{(2)n} & \cdots & \mathbf {X_{(n)n}} &\longrightarrow & \mathbf {X_{(n)n}} \end{matrix} \end{align*}$$$$Owing to the mathematical foundation and effectiveness discussions of Takahasi 21 and Takahasi and Wakimoto, 22 it is noted that RSS method could enhance the efficiency of the estimation process in a cost‐effective manner and that the accuracy of RSS estimators may be compromised when the ranking process is prone to errors. The RSS scenario was also discussed by many authors, see, for example, the works of Dell and Clutter, 23 Basikhasteh et al., 24 Bouza‐Herrera and Al‐Omari, 25 Esemen and Gürler, 26 and Zamanzade et al …”

New mixed ranked set sampling variations

“…Recently, Al‐Nasser and Al‐Omari (2018) introduced MiniMax RSS (MMRSS) which is an efficient mixed RSS and illustrated that MMRSS is more precise than SRS and requires fewer units to be ranked than RSS. For more details and applications about RSS, see, for example, Johnson et al (1993), Kaur et al (1995), Aragon et al (1999), Chen et al (2003), Bouza‐Herrera and Al‐Omari (2018), Al‐Omari (2011, 2012, 2013, 2014), Hanandeh and Al‐Nasser (2020, 2021), and references cited therein. These new developments made RSS applicable in a much wider range of fields than originally intended.…”