What is the purpose of robust regression?

Robust regression is an alternative to least squares regression when data is contaminated with outliers or influential observations and it can also be used for the purpose of detecting influential observations. Please note: The purpose of this page is to show how to use various data analysis commands.

What is Huber regression?

Huber regression (Huber 1964) is a regression technique that is robust to outliers. The idea is to use a different loss function rather than the traditional least-squares; we solve. minimizeβ∑mi=1ϕ(yi−xTiβ) for variable β∈Rn, where the loss ϕ is the Huber function with threshold M>0, ϕ(u)={u2if |u|≤M2Mu−M2if |u|>M.

How do you do robust regression?

The following step-by-step example shows how to perform robust regression in R for a given dataset.

  1. Step 1: Create the Data. First, let’s create a fake dataset to work with: #create data df <- data.
  2. Step 2: Perform Ordinary Least Squares Regression.
  3. Step 3: Perform Robust Regression.

Is linear regression robust to outliers?

Why Use Robust Regression? Robust linear regression is less sensitive to outliers than standard linear regression. Standard linear regression uses ordinary least-squares fitting to compute the model parameters that relate the response data to the predictor data with one or more coefficients.

What is the difference between a regression and a robust regression?

Robust regression provides an alternative to least squares regression that works with less restrictive assumptions. Specifically, it provides much better regression coefficient estimates when outliers are present in the data. Outliers violate the assumption of normally distributed residuals in least squares regression.

What is robust regression analysis?

In robust statistics, robust regression is a form of regression analysis designed to overcome some limitations of traditional parametric and non-parametric methods. Regression analysis seeks to find the relationship between one or more independent variables and a dependent variable.

Is Huber loss better?

Huber Loss is often used in regression problems. Compared with MSE, Huber Loss is less sensitive to outliers as if the loss is too much it changes quadratic equation to linear and hence is a combination of both MSE and MAE.

Why is Huber loss used?

In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for classification is also sometimes used.

What is the scale in robust regression?

However, the advantage of the robust approach comes to light when the estimates of residual scale are considered. For ordinary least squares, the estimate of scale is 0.420, compared to 0.373 for the robust method.

Why linear regression works poorly with outliers?

It is sensitive to outliers and poor quality data—in the real world, data is often contaminated with outliers and poor quality data. If the number of outliers relative to non-outlier data points is more than a few, then the linear regression model will be skewed away from the true underlying relationship.

What are the assumptions of linear regression?

There are four assumptions associated with a linear regression model: Linearity: The relationship between X and the mean of Y is linear. Homoscedasticity: The variance of residual is the same for any value of X. Independence: Observations are independent of each other.