ROBUST TEST BASED ON NONLINEAR REGRESSION QUANTILE ESTIMATORS

- Journal title : Communications of the Korean Mathematical Society
- Volume 20, Issue 1, 2005, pp.145-159
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2005.20.1.145

Title & Authors

ROBUST TEST BASED ON NONLINEAR REGRESSION QUANTILE ESTIMATORS

CHOI, SEUNG-HOE; KIM, KYUNG-JOONG; LEE, MYUNG-SOOK;

CHOI, SEUNG-HOE; KIM, KYUNG-JOONG; LEE, MYUNG-SOOK;

Abstract

In this paper we consider the problem of testing statistical hypotheses for unknown parameters in nonlinear regression models and propose three asymptotically equivalent tests based on regression quantiles estimators, which are Wald test, Lagrange Multiplier test and Likelihood Ratio test. We also derive the asymptotic distributions of the three test statistics both under the null hypotheses and under a sequence of local alternatives and verify that the asymptotic relative efficiency of the proposed test statistics with classical test based on least squares depends on the error distributions of the regression models. We give some examples to illustrate that the test based on the regression quantiles estimators performs better than the test based on the least squares estimators of the least absolute deviation estimators when the disturbance has asymmetric and heavy-tailed distribution.

Keywords

nonlinear regression quantiles estimators;Wald test;Lagrange multiplier test;likelihood ratio test;

Language

English

Cited by

References

1.

A. R. Gallant, Nonlinear Regression Models , John Wiley and Sons, 1987

2.

Huber, Robust Statistics , John Wiley and Sons, 1981

3.

R. Koenker and G. Bassett, Regression Quantiles, Econometrica 46 (1978), 33- 50

4.

R. Koenker, Robust Tests for Heterocedasticity based on Regression Quantiles, Econometrica 50 (1982), 43-61

5.

J. Jureckova and B. Prochazka, Regression quantiles and trimmed least squares estimators in nonlinear regression model , Nonparametric Statistics 3 (1994), 201-222

6.

E. L. Lehmann, Testing Statistical Hypotheses , John Wiley and Sons, 1986

7.

Z. J. Liu, Nonparametric Estimates of the Nuisance Parameter in the LAD Tests, Communication in Statistics-A, 21 (1992), 861-881

8.

G. A. F. Seber and C. J. Wild, Nonlinear Regression, John Wiley and Sons, 1989