Robust Regression

Robust regression is a statistical method that is used to estimate the parameters of a linear regression model in the presence of outliers or influential points. Outliers are data points that are significantly different from the rest of the data, and they can have a large impact on the results of a linear regression analysis. Influential points are data points that have a large impact on the results of a linear regression analysis, even though they may not be outliers. Robust regression methods are designed to minimize the impact of outliers and influential points on the results of a linear regression analysis.

Types of Robust Regression

There are several different types of robust regression methods, including:

• Least absolute deviations (LAD) regression: LAD regression minimizes the sum of the absolute deviations of the residuals from the fitted line. This makes LAD regression less sensitive to outliers than ordinary least squares (OLS) regression, which minimizes the sum of the squared residuals.
• Least trimmed squares (LTS) regression: LTS regression minimizes the sum of the squared residuals of a subset of the data, typically the 50% of the data with the smallest residuals. This makes LTS regression less sensitive to outliers than OLS regression, but it is more computationally intensive than LAD regression.
• Quantile regression: Quantile regression estimates the median or other quantile of the response variable, rather than the mean. This makes quantile regression less sensitive to outliers than OLS regression, and it can be used to analyze data with a non-normal distribution.

Applications of Robust Regression

Robust regression methods are used in a wide variety of applications, including: