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Robust estimation in nonlinear regression via minimum distance method

Research output: Contribution to journalJournal article

Published

Journal publication date1996
JournalMathematical Methods of Statistics
Volume5
Number of pages14
Pages99-112
Original languageEnglish

Abstract

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.