# M-Estimation Method Based Asymmetric Objective Function

## TL;DR

This paper introduces an asymmetric M-estimation method with a novel objective function to better model skewed data and improve robustness in parameter estimation, demonstrated through simulations and real data applications.

## Contribution

It proposes a new asymmetric objective function for M-estimation, enhancing robustness and accuracy in skewed data modeling compared to traditional symmetric methods.

## Key findings

- Asymmetric M-estimators outperform Huber estimators on skewed data.
- The method provides robust estimates for location, scale, and skewness.
- Application to regression shows improved modeling of skewed relationships.

## Abstract

The asymmetric objective function is proposed as an alternative to Huber objective function to model skewness and obtain robust estimators for the location, scale and skewness parameters. The robustness and asymptotic properties of the asymmetric M-estimators are explored. A simulation study and real data examples are given to illustrate the performance of proposed asymmetric M-estimation method over the symmetric M-estimation method. It is observed from the simulation results that the asymmetric M-estimators perform better than Huber M-estimators when the data have skewness. The application on regression is also considered.