NONLINEAR ASYMMETRIC LEAST SQUARES ESTIMATORS

  • Park, Seung-Hoe (Department of General Studies, Hankuk Aviation University) ;
  • Kim, Hae-Kyung (Department of Mathematics, Yonsei University) ;
  • Lee, Young (Department of Mathematics, Yonsei University)
  • Published : 2003.03.01

Abstract

In this paper, we consider the asymptotic properties of asymmetric least squares estimators for nonlinear regression models. This paper provides sufficient conditions for strong consistency and asymptotic normality of the proposed estimators and derives asymptotic relative efficiency of the pro-posed estimators to the regression quantile estimators. We give some examples and results of a Monte Carlo simulation to compare the asymmetric least squares estimators with the regression quantile estimators.

Keywords

References

  1. Journal of the American Statistical Association v.77 An empirical quantile function for linear models with iid errors Basset, G.;Koenker, R.
  2. Econometric Theory v.2 Strong consistency of regression quantile and related empirical process Basset, G.;Koenker, R.
  3. The Journal of Human Resources v.27 Recent advances in quantiles regression model Buchinsky, M.
  4. Journal of the Korean Statistical Society v.30 nonlinear regression quantiles estimation Choi, S.H.;Kim, H. K.;Park, K. O.
  5. The Annals of Mathematical Statistics v.40 Asymptotic properties of nonlinear least squares estimations Jennrich, R.
  6. Nonparametric Statistics v.3 Regression quantiles and trimmed least squares estimators in nonlinear regression model Jureckova, J.;Prochazka, B.
  7. Econometrica v.46 Regression Quantiles Koenker, R.;Basset, G.
  8. Asymmetric least squares estimation and testing v.55 Asymmetric least squares estimation and testing Newey, W. K.;Powell, L.
  9. The Annals of Statistics v.10 The consistency of nonlinear regression mimimizing the $L_1-norm$ Oberhofer, W.
  10. Nonlinear Regression Seber, G. A. F.;Wild, C. J.
  11. Large Sample MEthods in Statistics Sen, P. K.;Singer, J. M.
  12. Approzimation Theorems of Mathematical Statistics Serfling, R. J.
  13. The Annals of Statistics v.9 Asymptotic theory of nonlinear least squares estimation Wu, C. F. J.