H-relative error estimation approach for multiplicative regression model with random effect

Relative error approaches are more of concern compared to absolute error ones such as the least square and least absolute deviation, when it needs scale invariant of output variable, for example with analyzing stock and survival data. An h-relative error estimation method via the h-likelihood is developed to avoid heavy and intractable integration for a multiplicative regression model with random effect. Statistical properties of the parameters and random effect in the model are studied. To estimate the parameters, we propose an h-relative error computation procedure. Numerical studies including simulation and real examples show the proposed method performs well.