The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Saddlepoint Approximations to the Distribution Function of Non-homogeneous Quadratic Forms

비동차 이차형식의 분포함수에 대한 안장점근사

  • Na Jong-Hwa (Department of Information and Statistics & Institute for Basic Sciences, Chungbuk National University) ;
  • Kim Jeong-Soak (Principal Researcher, Information and Communication Dept., Health Insurance B/D)
  • 나종화 (충북대학교 정보통계학과 & 기초과학연구소) ;
  • 김정숙 (건강보험심사평가원)
  • Published : 2005.03.01
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Abstract

In this paper we studied the saddlepoint approximations to the distribution of non-homogeneous quadratic forms in normal variables. The results are the extension of Kuonen's which provide the same approximations to homogeneous quadratic forms. The CGF of interested statistics and related properties are derived for applications of saddlepoint techniques. Simulation results are also provided to show the accuracy of saddlepoint approximations.

본 논문에서는 다변량 정규분포하에서 비동차(non-homogeneous) 이차형식의 분포 함수에 대한 안장점근사법을 다루었다. 이는 Kuonen (1999)의 동차(homogeneous) 이차형식에 대한 안장점근사를 비동차의 경우로 확장한 것이다. 안장점근사의 적용을 위해 비동차 이차형식의 누율생성함수 및 관련 성질들을 유도하였다. 모의실험을 통해 안장점근사의 정도가 매우 뛰어남을 확인하였다.

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References

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