Weighted Estimation of Quantiles Using Unbalanced Ranked Set Sampling

Zhang, Liangyong; Dong, Xianjun; Xu, Xingzhong; Cui, Lirong

doi:10.1080/16843703.2014.11673345

Cited by 7 publications

(1 citation statement)

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“…Some works in the literature attempt to address the issue of the optimal cycle size m assuming the set size r is fixed (Zhang et al., ; Wolfe et al., ; Öztürk and Wolfe, ). In our current research, we assume all cycle sizes for selecting each judgment ordered value are the same, which is denoted as the balanced RSS scheme.…”

Section: Summary and Discussionmentioning

confidence: 99%

Improved nonparametric estimation of the optimal diagnostic cut‐off point associated with the Youden index under different sampling schemes

2016

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A diagnostic cut-off point of a biomarker measurement is needed for classifying a random subject to be either diseased or healthy. However, the cut-off point is usually unknown and needs to be estimated by some optimization criteria. One important criterion is the Youden index, which has been widely adopted in practice. The Youden index, which is defined as the maximum of (sensitivity + specificity -1), directly measures the largest total diagnostic accuracy a biomarker can achieve. Therefore, it is desirable to estimate the optimal cut-off point associated with the Youden index. Sometimes, taking the actual measurements of a biomarker is very difficult and expensive, while ranking them without the actual measurement can be relatively easy. In such cases, ranked set sampling can give more precise estimation than simple random sampling, as ranked set samples are more likely to span the full range of the population. In this study, kernel density estimation is utilized to numerically solve for an estimate of the optimal cut-off point. The asymptotic distributions of the kernel estimators based on two sampling schemes are derived analytically and we prove that the estimators based on ranked set sampling are relatively more efficient than that of simple random sampling and both estimators are asymptotically unbiased. Furthermore, the asymptotic confidence intervals are derived. Intensive simulations are carried out to compare the proposed method using ranked set sampling with simple random sampling, with the proposed method outperforming simple random sampling in all cases. A real data set is analyzed for illustrating the proposed method.

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Section: Summary and Discussionmentioning

confidence: 99%