#### DMCA

## Regression Analysis for Data Containing Outliers and High Leverage Points

### Citations

1736 |
Robust regression and outlier detection
- Rousseeuw, Leroy
- 2003
(Show Context)
Citation Context ...ncorrect observations (i.e. arbitrarily large observations) an estimator can handle before giving an arbitrarily large result. The range of breakdown point is zero to 0.5 (0 ≤ breakdown point ≤ 0.5) (=-=Rousseeuw & Leroy, 1987-=-). The smallest possible breakdown point is 1/n, that is, a single observation can distort the estimator so badly that it is of no practical use to regression model-builder. The breakdown point of OLS... |

1550 |
Applied Regression Analysis
- Draper, Smith
- 1981
(Show Context)
Citation Context ...s an n×1 vector of the observations , X is an n×(k+1) matrix of the levels of the regressor variables, β is a (k+1)×1 vector of the regression coefficients, and is an n × 1 vector of random errors (=-=Drapper & Smith, 1998-=-). Parameter Estimation A number of procedures have been developed for parameter estimation and inference in linear regression. Among them ordinary least squares (OLS) is the simplest and very common ... |

649 | Least median of squares regression
- Rousseeuw
- 1984
(Show Context)
Citation Context ...iables. On the other hand, an observation with an extreme value on a predictor variable is a point with high leverage. Leverage is a measure of how far an independent variable deviates from its mean (=-=Rousseeuw, 1984-=-). A number of methods have been developed to diagnosis outliers. Among them studentized residuals are frequently used. Studentized residuals can be obtained as, Studentized residual = ei S (i) √ 1 − ... |

381 |
Introduction to linear regression analysis.
- Montgomery, Peck, et al.
- 2015
(Show Context)
Citation Context ...stributions tend to generate outliers, and these outliers may have a strong influence on the method of least squares in the sense that they “pull" the regression equation too much in their direction (=-=Montgomery, Peck, & Vining, 2012-=-). The purpose of this study is to determine the appropriate estimation methods of regression parameter for this case. The paper is organized into four sections: the first introduces a brief descripti... |

303 |
Robust regression: Asymptotics, conjectures and Monte
- Huber
- 1973
(Show Context)
Citation Context ...fficiency of a robust estimator can be thought of as the residual mean square obtained from OLS divided by the residual mean square from the robust procedure. M Estimation M estimation introduced by (=-=Huber, 1973-=-) is the simplest approach both computationally and theoretically. Instead of minimizing sum of squares of the residuals, M estimator minimizes a sum of less rapidly increasing function (weight functi... |

260 |
Robust regression using iteratively reweighted leastsquares,
- Holland, Welsch
- 1977
(Show Context)
Citation Context ...essentially the same results as least squares when the underlying distribution in normal and there are no outliers. Roughly speaking, it is a form of weighted and reweighted least squares regression (=-=Holland & Welsch, 1977-=-). A number of robust estimation have been introduced in the last three decades. Among them M estimation and MM estimation are frequently used. A robust estimator has two important properties, namely ... |

88 |
Robust Regression by Means of S-Estimators: in
- Rousseeuw, Yohai
- 1984
(Show Context)
Citation Context ...point. MM estimator is based on the following two estimators: Least Trimmed Squares (LTS) Estimator and S Estimator. LTS Estimator (Rousseeuw, 1984) is a high breakdown value method. And S estimator (=-=Rousseeuw & Yohai, 1984-=-)) is a high breakdown value method with higher statistical efficiency than LTS estimation. As a result MM estimation can be defined by a two stage procedure: 1. The first step is to compute an initia... |

7 |
Basic Econometrics. 4th
- Gujarati
- 2003
(Show Context)
Citation Context ... the explanatory variables, with a view of estimating and/or predicting the (population) mean or average value of the former in terms of the known or fixed (in repeated sampling) values of the later (=-=Gujarati, 2003-=-). Suppose that we have a response variable y and a number of explanatory variables x1,x2,..., xk that may be related to y. Then regression model for y can be written as yi = β0 + β1xi1 + β2xi2 + ... ... |