The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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On prediction intervals for binomial data

이항자료에 대한 예측구간

  • Ryu, Jea-Bok (Department of Statistics, College of Science & Engineering, Cheongju University)
  • 류제복 (청주대학교 이공대학 통계학과)
  • Received : 2021.05.14
  • Accepted : 2021.05.14
  • Published : 2021.08.31
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Abstract

Wald, Agresti-Coull, Jeffreys, and Bayes-Laplace methods are commonly used for confidence interval of binomial proportion are applied for prediction intervals. We used coverage probability, mean coverage probability, root mean squared error, and mean expected width for numerical comparisons. From the comparisons, we found that Wald is not proper as for confidence interval and Agresti-Coull is too conservative to differ from confidence interval. However, Jeffrey and Bayes-Laplace are good for prediction interval and Jeffrey is especially desirable as for confidence interval.

신뢰구간 추정에 널리 사용되고 있는 Wald, Agresti-Coull, 그리고 베이지안 방법인 Jeffrey와 Bayes-Laplace를 예측구간에 적용하였다. 네 가지 방법의 수치적 비교를 위해서 포함확률, 평균포함확률, 평균제곱오차의 제곱근, 그리고 평균기대폭을 사용하였다. 비교결과 Wald 방법은 신뢰구간에서와 마찬가지로 예측구간에서도 바람직하지 않았고 신뢰구간에서 선호되던 Agresti-Coull 방법은 예측구간에서는 너무 보수적이라 적절치 않다. 반면에 Jeffrey와 Bayes-Laplace 방법은 적절하였고, 특히 Jeffrey 방법은 신뢰구간의 경우에서와 마찬가지로 예측구간에서도 바람직하였다.

Keywords

Acknowledgement

이 논문은 2012년도에 청주대학교 산업과학연구소가 지원한 학술연구조성비(특별연구과제)에 의해 연구되었음.

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