Empirical likelihood for least absolute relative error regression

Multiplicative regression models are useful for analyzing data with positive responses, such as wages, stock prices and lifetimes, that are particularly common in economic, financial, epidemiological and social studies. Recently, the least absolute relative error (LARE) estimation was proposed to be a useful alternative to the conventional least squares (LS) or least absolute deviation (LAD). However, one may resort to the time-consuming resampling methods for the inference of the LARE estimation. This paper proposes an empirical likelihood approach towards constructing confidence intervals/regions of the regression parameters for the multiplicative models. The major advantage of the proposal is its ability of internal studentizing to avoid density estimation. And it is computationally fast. Simulation studies investigate the effectiveness of the proposed method. An analysis of the body fat data is presented to illustrate the new method.