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Multidimensional indices Nonlinear Signed-Rank regression

*Brice Merlin Nguelifack, Auburn University 


We consider a nonlinear regression model when the index variable is multidimensional. Sufficient conditions on the non- linear function are given under which the Signed-Rank estimators are strongly consistent and asymptotically normally distributed. These sufficient conditions are satisfied by harmonic type functions, which are also of interest in the one dimensional index case where Wu’s (Asymptotic theory of non-linear least-squares estima- tion, Ann. Statist. 9 (1981) 501 - 513) and Jennrich’s (Asymptotic properties of nonlinear least-squares estimators, Ann. Math. Statist. 40 (1969) 633 - 643) sufficient conditions are not applicable.