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A product relative error estimation method for single index regression modelis proposed as an alternative to absolute error methods, such as the leastsquare estimation and the least absolute deviation estimation. It is scaleinvariant for outcome and covariates in the model. Regression coefficients areestimated via a two-stage procedure and their statistical properties such asconsistency and normality are studied. Numerical studies including simulationand a body fat example show that the proposed method performs well.

A relative error estimation approach for single index model