Journal of the Korean Geographical Society (대한지리학회지)

The Korean Geographical Society (대한지리학회)
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A Generalized Procedure to Extract Higher Order Moments of Univariate Spatial Association Measures for Statistical Testing under the Normality Assumption

일변량 공간 연관성 측도의 통계적 검정을 위한 일반화된 고차 적률 추출 절차: 정규성 가정의 경우

  • Lee, Sang-Il (Department of Geography Education, Seoul National University)
  • 이상일 (서울대학교 사범대학 지리교육학과)
  • Published : 2008.06.30
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Abstract

The main objective of this paper is to formulate a generalized procedure to extract the first four moments of univariate spatial association measures for statistical testing under the normality assumption and to evaluate the viability of hypothesis testing based on the normal approximation for each of the spatial association measures. The main results are as follows. First, predicated on the previous works, a generalized procedure under the normality assumption was derived for both global and local measures. When necessary matrices are appropriately defined for each of the measures, the generalized procedure effectively yields not only expectation and variance but skewness and kurtosis. Second, the normal approximation based on the first two moments for the global measures fumed out to be acceptable, while the notion did not appear to hold to the same extent for their local counterparts mainly due to the large magnitude of skewness and kurtosis.

이 논문의 주요 목적은 정규성 가정 하에 일변량 공간 연관성 측도의 첫 번째 네 적률을 구해내는 일반화된 추출 절차를 정식화하고, 그것을 바탕으로 각 측도의 가설 검정을 위해 정규근사가 갖는 가능성과 한계를 평가하는 것이다. 중요 연구 결과는 다음과 같다. 첫째, 이전의 연구에 기반함으로써, 정규성 가정 하에 전역적 측도와 국지적 측도에 모두 적용될 수 있는 일반화된 적률 추출절차가 도출되었다. 개별 공간 연관성 측도를 위한 필수적인 메트릭스가 적절히 정의되었을 때, 일반화된 유의성 검정 방법은 각 공간 연관성 측도의 기대값과 분산은 물론 첨도와 왜도를 효과적으로 산출하였다. 둘째, 첫 번째 두 적률에 근거한 정규근사 방법은 전역적 통계량에 대해서는 유효한 것으로 판명되었지만, 국지적 통계량에 대해서는 매우 높은 왜도와 첨도로 말미암아 그 유효성이 현저히 떨어지는 것으로 드러났다.

Keywords

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