Communications for Statistical Applications and Methods

  • 제19권3호
  • /
  • Pages.405-414
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  • 2012
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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층화모집단 평균에 대한 붓스트랩 추론

On Statistical Inference of Stratified Population Mean with Bootstrap

  • 허태영 (충북대학교 정보통계학과) ;
  • 이두리 (충북대학교 정보통계학과) ;
  • 조중재 (충북대학교 정보통계학과)
  • Heo, Tae-Young (Department of Information Statistics, Chungbuk National University) ;
  • Lee, Doo-Ri (Department of Information Statistics, Chungbuk National University) ;
  • Cho, Joong-Jae (Department of Information Statistics, Chungbuk National University)
  • 투고 : 2012.03.08
  • 심사 : 2012.03.29
  • 발행 : 2012.05.31
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초록

층화확률추출은 모집단을 어떤 층화기준에 의해 여러 층으로 분할한 다음 각 층으로부터 독립적으로 표본을 임의추출하는 방법으로 여러 가지 장점을 가지고 있어 실제 조사에서 많이 활용되고 있다. 본 연구에서는 대규모 표본조사에서 많이 사용하고 있는 층화확률추출을 사용하여 추출된 표본을 통해 모평균에 대한 붓스트랩 추정량과 신뢰구간 및 가설검정 등 통계적 추론에 대하여 연구하였다. 층화모집단에서의 모평균의 추정량과 관련된 극한 분포이론들을 기초로 붓스트랩 일치성을 근거로 층화 모평균에 대해 표준 붓스트랩 방법, 백분위수 붓스트랩 방법, 스튜던트화 붓스트랩 방법을 활용한 신뢰구간과 붓스트랩 가설검정 방법을 제안하였으며, 모의실험을 통해 신뢰구간 추정 방법들의 유효성을 확인하였다.

In a stratified sample, the sampling frame is divided into non-overlapping groups or strata (e.g. geographical areas, age-groups, and genders). A sample is taken from each stratum, if this sample is a simple random sample it is referred to as stratified random sampling. In this paper, we study the bootstrap inference (including confidence interval) and test for a stratified population mean. We also introduce the bootstrap consistency based on limiting distribution related to the plug-in estimator of the population mean. We suggest three bootstrap confidence intervals such as standard bootstrap method, percentile bootstrap method and studentized bootstrap method. We also suggest a bootstrap test method computing the $ASL_{boot}$(Achieved Significance Level). The results of estimation are verified using simulation.

키워드

참고문헌

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