On estimation of $$P\left( X > Y \right) $$PX>Y based on judgement post stratification

Ali Dastbaravarde () and Ehsan Zamanzade ()
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Ali Dastbaravarde: Yazd University
Ehsan Zamanzade: University of Isfahan

Statistical Papers, 2020, vol. 61, issue 2, No 12, 767-785

Abstract: Abstract We propose an unbiased estimator for $$P\left( X>Y\right) $$PX>Y and obtain an exact expression for its variance, based on judgement post stratification (JPS) sampling scheme. We then prove that the introduced estimator is consistent and establish its asymptotic normality. We show that the proposed estimator is at least as efficient asymptotically as its counterpart in simple random sampling (SRS), regardless of the quality of the rankings. For finite sample sizes, a Monte Carlo simulation study and a real data set are employed to show the preference of the JPS estimator to its SRS competitor in a wide range of settings.

Keywords: Judgement post stratification; Reliability analysis; Simple random sampling; Asymptotic normality; 62D05; 62N05; 62G05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00362-017-0962-0

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