منابع مشابه
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...
متن کاملRobust 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...
متن کاملRobust 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...
متن کاملRobust weighted LAD regression
The least squares linear regression estimator is well-known to be highly sensitive to unusual observations in the data, and as a result many more robust estimators have been proposed as alternatives. One of the earliest proposals was least-sum of absolute deviations (LAD) regression, where the regression coefficients are estimated through minimization of the sum of the absolute values of the re...
متن کاملRobust L1 orthogonal regression
Assessing the linear relationship between a set of continuous predictors and a continuous response is a well studied problem in statistics and is applied in many data mining situations. L2 based methods such as ordinary least squares and principal components regression can be used to determine this relationship. However, both of these methods become impaired when multicollinearity is present. T...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1987
ISSN: 0090-5364
DOI: 10.1214/aos/1176350255