The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Saddlepoint approximation to the distribution function of quadratic forms based on multivariate skew-normal distribution

다변량 왜정규분포 기반 이차형식의 분포함수에 대한 안장점근사

  • Na, Jonghwa (Department of Information & Statistics, Chungbuk National University)
  • Received : 2016.02.03
  • Accepted : 2016.04.25
  • Published : 2016.06.30
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Abstract

Most of studies related to the distributions of quadratic forms are conducted under the assumption of multivariate normal distribution. In this paper, we suggested an approximation to the distribution of quadratic forms based on multivariate skew-normal distribution as alternatives for multivariate normal distribution. Saddlepoint approximations are considered and the accuracy of the approximations are verified through simulation studies.

이차형식 통계량의 분포함수에 대한 연구는 주로 다변량 정규분포의 가정하에서 진행되어 왔다. 최근 다변량 정규분포를 포함하는 다변량 왜정규분포에 대한 연구가 활발하다. 본 논문에서는 다변량 왜정규분포의 가정하에서 이차형식 통계량의 분포함수에 대한 근사를 다루었다. 근사의 방법으로는 소표본에서도 정확도가 뛰어난 근사법으로 알려진 안장점근사를 사용하였으며, 모의실험을 통해 그 정도를 확인하였다.

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References

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