TY - JOUR

T1 - Robust estimation in nonlinear regression via minimum distance method

AU - Mukherjee, Kanchan

PY - 1996

Y1 - 1996

N2 - We study the asymptotic properties of a general class of minimum distance estimators based on L2 norms of weighted empirical processes in nonlinear regression models. In particular, the asymptotic uniform quadratic structure of the minimum distance statistics and the asymptotic representation of the estimator are established under weak conditions on the nonlinear function and under some non-i.i.d. structures of the error variables. The results imply the asymptotic normality of the estimator and its qualitative robustness. Applications are given to the problem of goodness-of-fit tests for the error distribution.

AB - We study the asymptotic properties of a general class of minimum distance estimators based on L2 norms of weighted empirical processes in nonlinear regression models. In particular, the asymptotic uniform quadratic structure of the minimum distance statistics and the asymptotic representation of the estimator are established under weak conditions on the nonlinear function and under some non-i.i.d. structures of the error variables. The results imply the asymptotic normality of the estimator and its qualitative robustness. Applications are given to the problem of goodness-of-fit tests for the error distribution.

KW - Minimum distance method

M3 - Journal article

VL - 5

SP - 99

EP - 112

JO - Mathematical Methods of Statistics

JF - Mathematical Methods of Statistics

SN - 1934-8045

ER -