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Improved Nonparametric Estimation Using Partially Ordered Sets

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Book cover Statistical Methods and Applications in Forestry and Environmental Sciences

Part of the book series: Forum for Interdisciplinary Mathematics ((FFIM))

Abstract

Ranked set sampling (RSS) is a cost efficient design that has been widely used in agriculture, forestry, ecological and environmental sciences. Frey (Environmental and Ecological Statistics 19(3):309–326, 2012) proposed a sampling scheme based on to allow for partially ordered sets. This scheme permits a ranker to declare ties and then record the tie structure for potential use in statistical analysis. We first introduce two nonparametric maximum likelihood estimators (MLEs) of the population cumulative distribution function (CDF) that incorporate the information for partially ordered sets. We compare the proposed MLEs with the standard nonparametric MLE of the CDF (without utilizing tie information) via Monte Carlo simulation. Motivated by good performance of the new CDF estimators, we further derive two mean estimators for partially ordered sets. Our numerical results from both simulation and real data show that the proposed estimators outperform their competitors provided that the quality of ranking is not low.

The authors wish it to be known that, in their opinion, they both should be equally regarded as the corresponding authors.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Isfahan, 81746-73441, Isfahan, Iran

    Ehsan Zamanzade

  2. Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, Dallas, TX, 75275, USA

    Xinlei Wang

Authors
  1. Ehsan Zamanzade
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  2. Xinlei Wang
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Corresponding author

Correspondence to Xinlei Wang .

Editor information

Editors and Affiliations

  1. Indian Council of Forestry Research and Education, Dehradun, Uttarakhand, India

    Girish Chandra

  2. Indian Council of Forestry Research and Education, Dehradun, Uttarakhand, India

    Raman Nautiyal

  3. Indian Agricultural Statistics Research Institute, New Delhi, Delhi, India

    Hukum Chandra

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Zamanzade, E., Wang, X. (2020). Improved Nonparametric Estimation Using Partially Ordered Sets. In: Chandra, G., Nautiyal, R., Chandra, H. (eds) Statistical Methods and Applications in Forestry and Environmental Sciences. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-1476-0_5

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