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M-Estimators in Regression Models

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Author(s): Muthukrishnan R | Radha Myilsamy

Journal: Journal of Mathematics Research
ISSN 1916-9795

Volume: 2;
Issue: 4;
Date: 2010;
Original page

ABSTRACT
Regression analysis plays a vital role in many areas of science. Almost all the regression analysis relies on the method of least squares for estimation of the parameters in the model. But this method constructed under specific assumptions, such as normality of the error distribution. When outliers are present in the data, this method of estimation, resulting in parameter estimates that do not provide useful information for the majority of the data. Robust regression analyses have been developed as an improvement to least square estimation in the presence of outliers. The main purpose of robust regression analysis is to fit a model that represents the information of the majority of the data. Many researchers have worked in this field and developed methods for these problems. The most commonly used robust estimators are Huber’s M-estimator, Hampel estimator, Tukey’s bisquare estimator etc. In this paper, an attempt is made to review such type of estimators and carried out a simulation study of these estimators in regression models. R code has been written for this purpose and illustrations are provided.
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