The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Robust confidence interval for random coefficient autoregressive model with bootstrap method

붓스트랩 방법을 적용한 확률계수 자기회귀 모형에 대한 로버스트 구간추정

  • Jo, Na Rae (Department of Information and Statistics, Chungbuk National University) ;
  • Lim, Do Sang (Division of Chronic Disease Control Prevention, Korea Centers for Disease Control & Prevention) ;
  • Lee, Sung Duck (Department of Information and Statistics, Chungbuk National University)
  • 조나래 (충북대학교 정보통계학과) ;
  • 임도상 (질병관리본부 만성질환관리과) ;
  • 이성덕 (충북대학교 정보통계학과)
  • Received : 2018.12.03
  • Accepted : 2018.12.11
  • Published : 2019.02.28
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Abstract

We compared the confidence intervals of estimators using various bootstrap methods for a Random Coefficient Autoregressive(RCA) model. We consider a Quasi score estimator and M-Quasi score estimator using Huber, Tukey, Andrew and Hempel functions as bounded functions, that do not have required assumption of distribution. A standard bootstrap method, percentile bootstrap method, studentized bootstrap method and hybrid bootstrap method were proposed for the estimations, respectively. In a simulation study, we compared the asymptotic confidence intervals of the Quasi score and M-Quasi score estimator with the bootstrap confidence intervals using the four bootstrap methods when the underlying distribution of the error term of the RCA model follows the normal distribution, the contaminated normal distribution and the double exponential distribution, respectively.

비선형 시계열인 확률계수 자기회귀(random coefficient autoregressive; RCA) 모형에 대하여 여러 가지 방법을 이용한 추정량의 신뢰구간 비교하였다. RCA 모형에 대하여 자료의 분포를 가정하지 않아도 되는 Quasi 스코어 추정량과 Huber, Tukey, Andrew, Hempal 4가지 유계함수를 이용한 M-Quasi 스코어 추정량을 제시하였다. 이러한 추정량에 대하여 표준 붓스트랩 방법, 백분위수 붓스트랩 방법, 스튜던트화 붓스트랩 방법, 하이브리드 붓스트랩 방법을 이용한 신뢰구간을 구하였다. 모의실험을 통하여 RCA 모형의 오차항의 분포가 정규분포, 오염정규분포, 이중지수분포를 따를 때 Quasi 스코어 추정량과 M-Quasi 스코어 추정량들의 근사적 신뢰구간과 네가지 붓스트랩 방법을 이용한 신뢰구간을 비교하였다.

Keywords

Table 5.1. Comparison of the simulated proportion that εt is standard normal distribution

GCGHDE_2019_v32n1_99_t0001.png 이미지

Table 5.2. Comparison of the simulated proportion that εt is double exponential distribution

GCGHDE_2019_v32n1_99_t0002.png 이미지

Table 5.3. Comparison of the simulated proportion that εt is contaminated normal distribution with 10% levelof contamination and 10 magnitude of contamination

GCGHDE_2019_v32n1_99_t0003.png 이미지

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