On Some Aspects of Spatial Ranked Set Sampling

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Date
2007
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Indian Agricultural Statistics Research Institute Indian Agricultural Research Institute New Delhi
Abstract
Ranked Set Sampling (RSS) as suggested by McIntyre (1952) when applied to spatially-correlated areal population fails to take into account the spatial correlation. Arbia (1990) suggested Dependent Unit Sequential Technique (DUST), a sample selection procedure for selection of areal units from spatially correlated population in which spatial correlation among the population units has been incorporated into sample selection procedure. In this thesis attempt has been made to propose a sample selection technique named as Spatial Ranked Set Sampling (SRSS) in which desirable features of both RSS and DUST have been incorporated. SRSS has characteristics of RSS such as randomization technique for better representation of population and additional information about ranking of units with in a set in the sample selection process. Also, the proposed SRSS incorporated spatial correlation as in case of DUST in the sample selection process. Four strategies of sample selection are proposed viz. (1) Ranked set sampling based on Spatial Clusters formed by DUST (RSCD), (2) Ranked set sampling based on Spatial Clusters formed by SRS (RSCS), (3) Ranked set sampling based on Spatial Sets formed by DUST (RSSD) and (4) Ranked set sampling based on Spatial Sets formed by SRS (RSSS). A spatial simulation study was carried out to empirically test the performance of SRSS with respect to the traditional sampling techniques. It has been found that SRSS always performs better in terms of efficiency with respect to SRS and there is sufficient gain in efficiency with respect to RSS in case of smaller set size which is generally recommended to avoid ranking errors. Among the four strategies of sample selection by SRSS, it has been observed that RSSD was the most efficient strategy as it had the lowest sampling variance. The availability of cheap and reliable data on a highly correlated auxiliary variable (NDVI) was put to use to carry out ratio estimation in all the four estimators. As expected, ratio estimator showed more gain than the corresponding estimator used earlier. Maximum gain was found for the ratio estimator of RSCS among all four ratio estimators considered. The results of the study point out that, in spatial surveys, a considerable gain in efficiency of the estimators could be achieved by using distance based sample selection strategies even when applying these for complex sampling schemes such as Ranked Set Sampling. The complex algorithms involved in the selection procedure of distance based sampling strategies could be solved with the use of advanced computing and software.
Description
t-7897
Keywords
Spatial Ranked ; Set Sampling
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