Information content of partially rank-ordered set samples

Armin Hatefi and Mohammad Jafari Jozani ()
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Armin Hatefi: The Fields Institute for Research in Mathematical Sciences
Mohammad Jafari Jozani: University of Manitoba

AStA Advances in Statistical Analysis, 2017, vol. 101, issue 2, No 1, 117-149

Abstract: Abstract Partially rank-ordered set (PROS) sampling is a generalization of ranked set sampling in which rankers are not required to fully rank the sampling units in each set, hence having more flexibility to perform the necessary judgemental ranking process. The PROS sampling has a wide range of applications in different fields ranging from environmental and ecological studies to medical research and it has been shown to be superior over ranked set sampling and simple random sampling for estimating the population mean. We study Fisher information content and uncertainty structure of the PROS samples and compare them with those of simple random sample (SRS) and ranked set sample (RSS) counterparts of the same size from the underlying population. We study uncertainty structure in terms of the Shannon entropy, Rényi entropy and Kullback–Leibler (KL) discrimination measures.

Keywords: Fisher information; Shannon entropy; Rényi entropy; Kullback–Leibler information; Misplacement probability matrix; 62B10; 62D05; 62E15; 62F99; 62J99 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10182-016-0277-9

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