Robust test based on nonlinear regression quantileestimators

Abstract

In this paper we consider the problem of testing sta-tistical hypotheses for unknown parameters in nonlinear regression models and propose three asymptotically equivalent tests based on regression quantiles estimators, which areWald test, Lagrange Mul- tiplier test and Likelihood Ratio test. We also derive the asymp-totic distributions of the three test statistics both under the null hypotheses and under a sequence of local alternatives and verify that the asymptotic relative e±ciency of the proposed test statis-tics 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.