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...

It is known that the tail index of a GARCH model is determined by a moment equation, which involves the underlying unknown parameters of the model. A tail index estimator can therefore be constructed by solving the sample moment equation with the unknown parameters being replaced by its...