# Least Product Relative Error Estimation

arXiv: https://arxiv.org/abs/1309.0220 · HTML: https://mlsanity.com/paper/1309.0220/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2013.

## Built on by (most cited first, 1 of 1)

- [Ratio-based Loss Functions](https://mlsanity.com/paper/2605.05808/) (2026)

## Abstract (arXiv)

A least product relative error criterion is proposed for multiplicative regression models. It is invariant under scale transformation of the outcome and covariates. In addition, the objective function is smooth and convex, resulting in a simple and uniquely defined estimator of the regression parameter. It is shown that the estimator is asymptotically normal and that the simple plugging-in variance estimation is valid. Simulation results confirm that the proposed method performs well. An application to body fat calculation is presented to illustrate the new method.