Abstract

This article concerns entropy estimation using judgment post stratification sampling. Some nonparametric estimators are developed and shown to be consistent. Monte Carlo simulations are used to compare these estimators with their competitors in simple random sampling. The results indicate the preference of the new estimators.

Highlights

  • Judgement post stratification (JPS) sampling scheme, introduced by MacEachern et al (2004), has wide applications in situations where auxiliary information is available to induce an additional ranking structure in simple random sampling (SRS) scheme

  • We developed some nonparametric entropy estimators for judgement post stratification sampling scheme

  • The estimators were obtained by using different cumulative distribution function estimators in the JPS setting

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Summary

Introduction

Judgement post stratification (JPS) sampling scheme, introduced by MacEachern et al (2004), has wide applications in situations where auxiliary information is available to induce an additional ranking structure in simple random sampling (SRS) scheme. A judgement post stratified sample can still be analyzed with standard SRS procedures This is very useful in situations in which the researcher believes that the ranking process is too poor or the required statistical method has not been developed yet for the JPS setting. Both RSS and JPS sampling schemes are useful in situations in which exact measurement of sample units is expensive or time-consuming but ranking them (without obtaining their precise values) is easy and cheap These situations frequently happen in forestry (Halls and Dell, 1966), medicine (Chen et al, 2005), environmental monitoring (Kvam, 2003; Nussbaum and Sinha, 1997; and Ozturk et al, 2005), reliability (Mahdizadeh and Zamanzade, 2016) and entomology (Howard et al, 1982).

Nonparametric estimation of CDF in JPS sampling scheme
Nonparametric estimation of entropy
Monte Carlo comparison
Conclusion
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