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

## TL;DR

This paper introduces an h-relative error estimation method for multiplicative regression models with random effects, emphasizing scale invariance and computational efficiency, validated through simulations and real data analysis.

## Contribution

It develops a novel h-relative error estimation approach using h-likelihood for multiplicative models with random effects, avoiding complex integrations.

## Key findings

- Method performs well in simulations
- Effective on real data examples
- Provides reliable parameter estimates

## Abstract

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.