The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Interval Estimation of Population Proportion in a Double Sampling Scheme

이중표본에서 모비율의 구간추정

  • 이승천 (한신대학교 정보통계학과) ;
  • 최병수 (한성대학교 멀티미디어학과)
  • Received : 20090800
  • Accepted : 20091000
  • Published : 2009.12.31
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Abstract

The double sampling scheme is effective in reducing the sampling cost. However, the doubly sampled data is contaminated by two types of error, namely false-positive and false-negative errors. These would make the statistical analysis more difficult, and it would require more sophisticate analysis tools. For instance, the Wald method for the interval estimation of a proportion would not work well. In fact, it is well known that the Wald confidence interval behaves very poorly in many sampling schemes. In this note, the property of the Wald interval is investigated in terms of the coverage probability and the expected width. An alternative confidence interval based on the Agresti-Coull's approach is recommended.

표본추출 비용의 절감을 위해 흔히 사용되는 이중표본추출방법은 대부분의 표본들이 2종류의 오류에 의해 오염이 되어 있어 통계적 분석이 상대적으로 용이하지 않다. 특히, 비율의 추론을 위한 중요한 분석 도구인 구간추정은 현재까지 우도추정량의 정규근사에 의존하는 Wald 방법만이 알려져 있으나 Wald 신뢰구간은 포함확률의 근사성 등에서 많은 문제가 있다는 것이 여러 연구에서 확인되고 있다. 본 연구에서는 이중표본추출에서 Wald 신뢰구간의 문제점을 파악하고 이에 대한 대안으로 Agresti-Coull 유형의 신뢰구간을 제시한다.

Keywords

References

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  2. Bayesian confidence intervals of proportion with misclassified binary data vol.42, pp.3, 2013, https://doi.org/10.1016/j.jkss.2012.09.001