The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Small Sample Asymptotic Inferences for Autoregressive Coefficients via Saddlepoint Approximation

안장점근사를 이용한 자기회귀계수에 대한 소표본 점근추론

  • Na, Jong-Hwa (Dept. of Information and Statistics & Institute for Basic Science Research, Chungbuk National University) ;
  • Kim, Jeong-Sook (Information & Communication Dept., Health Insurance)
  • 나종화 (충북대학교 정보통계학과 & 기초과학연구소) ;
  • 김정숙 (건강보험심사평가원 정보통신실)
  • Published : 2007.03.31
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Abstract

In this paper we studied the small sample asymptotic inference for the autoregressive coefficient in AR(1) model. Based on saddlepoint approximations to the distribution of quadratic forms, we suggest a new approximation to the distribution of the estimators of the noncircular autoregressive coefficients. Simulation results show that the suggested methods are very accurate even in the small sample sizes and extreme tail area.

본 논문에서는 1차 자기회귀모형에서 자기회귀계수에 대한 여러 가지 추정량들의 분포함수에 대한 근사 방법에 대해 연구하였다. 자기회귀계수의 여러 추정량들을 이차형식의 관점에서 이해하고, Na와 Kim(2005)에 의한 안장점근사의 결과를 이용한 새로운 근사법을 제시하였다. 이 방법은 정규근사를 비롯한 기존의 근사법과는 달리 추정량에 대한 근사분포의 유도과정이 불필요하며, 소표본은 물론 통계적 추론의 주요 관심영역에서의 근사정도가 매우 뛰어난 장점을 가지고 있다. 모의실험을 통해 Edgeworth 근사를 비롯한 기존의 여러 근사법보다 효율이 뛰어남을 확인하였다.

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References

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