Proposition of polytomous discrimination index and test statistics

다항판별지수와 검정통계량 제안

  • Received : 2016.02.12
  • Accepted : 2016.03.07
  • Published : 2016.03.31


There exist many real situations that statistical decision problems are classified into more than two categories. In these cases, the concordance statistics by the pair approach are mostly used. However, the expression of the classification of categories are ambiguous. Recently, the standardized evaluation data and re-expressed concordance statistics are defined and could be explained their meanings. They have still some non-specific problems for standard criteria of the statistics. Since these can be considered between result and truth categories additionally, two alternative concordance statistics might be proposed in this paper. Some advantages are founded that the proposed statistics could be discriminated all possible cases for two randomly selected categories. Moreover since the proposed statistics are represented with indicator functions, these could be transformed non-parametrically, so that these concordances are used for hypothesis testing.

현실세계의 예측 문제에서 세 범주 이상의 결과로 예측되는 경우가 많다. 이러한 경우에 대한 기존의 문헌연구에서는 부합성을 짝 접근방법으로 활용한 통계량은 범주의 뚜렷한 구분 없이 표현되었다. 최근 새롭게 표현한 평가자료와 이를 바탕으로 부합성을 재표현하여 통계량들을 새롭게 정의함으로써 직관적으로 의미 파악이 가능해졌지만 통계량들의 판단기준이 구체적이지 않은 문제점을 갖고 있다. 또한 이 통계량들은 가능한 부합성의 짝으로 구성되었지만 실제범주들간에서 예측범주들의 부합성을 추가적으로 고려할 수 있기에 이를 포함한 두 가지 통계량을 제안하였다. 제안한 통계량은 선택된 두 범주로부터 모든 가능한 경우들 사이를 판별하는 장점이 있다. 본 연구에서 제안한 두 가지 통계량은 지시함수로 표현되므로 비모수적 통계량으로 변환할 수 있다. 그러므로 부합성 통계량을 가설검정 방법으로 사용할 수 있음을 제안한다.



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