Asymptotic Properties of Regression Quanties Estimators in Nonlinear Models

비선형최소분위추정량의 점근적 성질

  • Choi, Seung-Hoe (Department of General Studies, Hankuk Aviation University) ;
  • Kim, Tae-Soo (Department of Industrial Engineering, Hangyang University) ;
  • Park, Kyung-Ok (Disital Printing Dvision, Samsung Electronics Co. Ltd)
  • 최승회 (한국항공대학교 교양학부) ;
  • 김태수 (한양대학교 산업공학과) ;
  • 박경옥 (삼성전자(주) 디지털프린팅(사))
  • Published : 2000.10.31

Abstract

In this paper, we consider the Regression Quantiles Estimators in nonlinear regression models. This paper provides the sufficient conditions for strong consistency and asymptotic normality of proposed estimation and drives asymptotic relative efficiency of proposed estimatiors with least square estimation. We give some examples and results of Monte Carlo simulation to compare least square and regression quantile estimators.

두 변수간의 함수관계를 연구하는 회귀분석에서 모수를 추정하기 위하여 가장 널리 사용되는 방법은 최소자승법이다. 그러나 최소자승법은 표본 평균처럼 약간의 이상치에도 민감하게 반응하여 강인성(robustness)을 만족하지 못함으로 새로운 추정량이 필요하다. 본 논문에서는 최소분위추정량과 최소분위추정량에 근거한 일차결합추정량의 점근적 성질을 연구하였다. 또한 최소자승추정량에 대해 제시된 추정량의 점근적 효율성을 구하고 모의실험을 통하여 최소분위추정량의 효율성을 조사하였다.

Keywords

References

  1. Econometric Theory v.2 Strong consistency of regression quantile and related emprical process Bassett, G.;Koenker, R.
  2. Journal of the Korean Statistical Society Nolinear regression quantiles estimation Choi S. H.;Kim, H. K.;Park, K. O.
  3. The Annal of Mathematical Statistics v.40 Asymptotic properties of nonlinear least squares estimations Jennrich, R.
  4. Journal of the Korean Statistical Society v.24 Asymptotic Properties of Nonlinear Least Absolute Deviation Estimators Kim, H. K.;Choi, S. H.
  5. Econometrica v.46 Regression Quantiles Koenker,R.;Bassett, G.
  6. The Annals of Statistics v.10 The consistency of nonlinear regression minimizing the L₁-norm Oberhofer, W.
  7. Journal of Multivariate Analysis v.50 Asymptotic behavior of regression quantiles in non-stationary dependent cases Portnoy, S.
  8. Journal of Econometrics v.32 Censored regression quantiles Powell, J. L.
  9. Journal of Multivariate Analysis v.54 Asymptotic normality of L₁-estimators in nonlinear regression Wang, J.
  10. The Annals of Statistics Asymptotic theory of nonlinear least squares estimation Wu, C. F.