What are the types of robust regression?

What are the different types of robust regression?

Robust regression techniques are designed to be less sensitive to outliers. The main types include:

1. M-estimators: Generalization of maximum likelihood estimators.
2. RANSAC: Random Sample Consensus, useful for fitting models in the presence of outliers.
3. Theil-Sen Estimator: A non-parametric method that is robust to outliers.
4. Huber Regression: Combines the ideas of least squares and absolute loss.

Can you explain M-estimators in more detail?

Sure! M-estimators are a broad class of estimators that generalize maximum likelihood estimators. They minimize a loss function, which can be chosen to reduce the influence of outliers. The loss function is typically a function of the residuals, and by using different loss functions, you can achieve different levels of robustness.

What is RANSAC and how does it work?

RANSAC, or Random Sample Consensus, is an iterative method to estimate parameters of a mathematical model from a dataset that contains outliers. It works by randomly selecting a subset of the data, fitting a model to this subset, and then determining how many points from the entire dataset fit this model well. This process is repeated multiple times to find the best model.

Are there any limitations to robust regression methods?

Yes, while robust regression methods are effective against outliers, they can be less efficient than ordinary least squares when the data is normally distributed without outliers. Additionally, some methods may require careful tuning of parameters to achieve optimal performance.