Bootrapping robust estimates of regression

Robust tests for linear regression models based on τ-estimates

ANOVA tests are the standard tests to compare nested linearmodels fitted by least squares. These tests are equivalent to likelihood ratio tests, so they have high power. However, least squares estimators are very vulnerable to outliers in the data, and thus the related ANOVA type tests are also extremely sensitive to outliers. Therefore, robust estimators can be considered to obtain a robust al...

Robust Regression

An introduction to robustness in statistics, with emphasis on its relevance to regression analysis. The weaknesses of the least squares estimator are highlighted, and the idea of error in data re ned. Properties such as breakdown, e ciency and equivariance are discussed and, through consideration of M, S and MM-estimators in relation to these properties, the progressive nature of robust estimat...

Robust Regression

1. Introduction One of the most important statistical tools is a linear regression analysis for many fields. Nearly all regression analysis relies on the method of least squares for estimation of the parameters in the model. A problem that we often encountered in the application of regression is the presence of an outlier or outliers in the data. Outliers can be generated by from a simple opera...

Robust Minimax Probability Machine Regression Robust Minimax Probability Machine Regression

We formulate regression as maximizing the minimum probability (Ω) that the true regression function is within ±2 of the regression model. Our framework starts by posing regression as a binary classification problem, such that a solution to this single classification problem directly solves the original regression problem. Minimax probability machine classification (Lanckriet et al., 2002a) is u...

Robust Regression Estimates in the Prediction of Latent Variables in Structural Equation Models