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