A relative error-based estimation with an increasing number of parameters

AbstractThe least product relative error (LPRE) estimator and test statistic to test linear hypotheses of regression parameters in the multiplicative regression model are studied when the number of covariate variables increases with the sample size. Some properties of the LPRE estimator and test statistic are obtained such as consistency, Bahadur presentation and asymptotic distributions. Furthermore, we extend the LPRE to a more general relative error criterion and provide their statistical properties. Numerical studies including simulations and two real examples show that the proposed estimation performs well.