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Showing 4 results for Collinearity
Forough Hajibagheri, Abdolrahman Rasekh, Mohammad Reza Akhoond,
Volume 8, Issue 1 (9-2014)
Abstract
The instability of the least squares parameter estimates under collinearity, might also causes instability of the residuals. If so, a large residual from a least squares fit might not be indicative of an erratic data point, and conversely. In order to resolve the problem of collinearity in the regression model, biased estimators like the Liu estimator is suggested. In this paper, it is shown that when Liu mean shift regression is used to mitigate the effect of the collinearity, the influence of some observations can be drastically changed and also the appropriate statistic for testing outliers is derived. In order to illustrate the performance of the proposed method, a real example is presented.
Abdolrahman Rasekh, Behzad Mansouri, Narges Hedayatpoor,
Volume 13, Issue 1 (9-2019)
Abstract
The study of regression diagnostic, including identification of the influential observations and outliers, is of particular importance. The sensitivity of least squares estimators to the outliers and influential observations lead to extending the regression diagnostic in order to provide criteria to assess the anomalous observations. Detecting influential observations and outliers in the presence of collinearity is a complicated task, in the sense that collinearity may cover some of the unusual data. One of the considerable methods to identify outliers is the mean shift outliers method. In this article, we extend the mean shift outliers method to the ridge estimates under linear stochastic restrictions, which is used to reduce the effect of collinearity, and to provide the test statistic to identify the outliers in these estimators. Finally, we show the ability of our proposed method using a practical example of real data.
Mahdi Roozbeh, Monireh Maanavi,
Volume 14, Issue 2 (2-2021)
Abstract
The popular method to estimation the parameters of a linear regression model is the ordinary least square method which, despite the simplicity of calculating and providing the BLUE estimator of parameters, in some situations leads to misleading solutions. For example, we can mention the problems of multi-collinearity and outliers in the data set. The least trimmed squares method which is one of the most popular of robust regression methods decreases the influence of outliers as much as possible. The main goal of this paper is to provide a robust ridge estimation in order to model dental age data. Among the methods used to determine age, the most popular method throughout the world is the modern modified Demirjian method that is based on the calcification of the permanent tooth in panoramic radiography. It has been shown that using the robust ridge estimator is leading to reduce the mean squared error in comparison with the OLS method. Also, the proposed estimators were evaluated in simulated data sets.
Zahra Zandi, Hossein Bevrani,
Volume 16, Issue 2 (3-2023)
Abstract
This paper suggests Liu-type shrinkage estimators in linear regression model in the presence of multicollinearity under subspace information. The performance of the proposed estimators is compared to Liu-type estimator in terms of their relative efficiency via a Monte Carlo simulation study and a real data set. The results reveal that the proposed estimators outperform better than the Liu-type estimator.
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