Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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On inference of multivariate means under ranked set sampling

  • Rochani, Haresh (Department of Biostatistics, Georgia Southern University) ;
  • Linder, Daniel F. (Department of Biostatistics, Augusta University) ;
  • Samawi, Hani (Department of Biostatistics, Georgia Southern University) ;
  • Panchal, Viral (Department of Biostatistics, Augusta University)
  • Received : 2017.05.31
  • Accepted : 2017.12.08
  • Published : 2018.01.31
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Abstract

In many studies, a researcher attempts to describe a population where units are measured for multiple outcomes, or responses. In this paper, we present an efficient procedure based on ranked set sampling to estimate and perform hypothesis testing on a multivariate mean. The method is based on ranking on an auxiliary covariate, which is assumed to be correlated with the multivariate response, in order to improve the efficiency of the estimation. We showed that the proposed estimators developed under this sampling scheme are unbiased, have smaller variance in the multivariate sense, and are asymptotically Gaussian. We also demonstrated that the efficiency of multivariate regression estimator can be improved by using Ranked set sampling. A bootstrap routine is developed in the statistical software R to perform inference when the sample size is small. We use a simulation study to investigate the performance of the method under known conditions and apply the method to the biomarker data collected in China Health and Nutrition Survey (CHNS 2009) data.

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