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Showing 4 results for Outliers
Ms Sara Jazan, Dr Seyyed Morteza Amini,
Volume 22, Issue 2 (3-2018)
Abstract
One of the factors affecting the statistical analysis of the data is the presence of outliers. The methods which are not affected by the outliers are called robust methods. Robust regression methods are robust estimation methods of regression model parameters in the presence of outliers. Besides outliers, the linear dependency of regressor variables, which is called multicollinearity, the large number of regressor variables with respect to sample size, specially in high dimensional sparse models, are problems which result in efficiency reduction of inferences in classical regression methods. In this paper, we first study the disadvantages of classical least squares regression method, when facing with outliers, multicollinearity and sparse models. Then, we introduce and study robust and penalized regression methods, as a solution to overcome these problems. Furthermore, considering outliers and multicollinearity or sparse models, simultaneously, we study penalized-robust regression methods. We examine the performance of different estimators introdused in this paper, through three different simulation studies. A real data set is also analyzed using the proposed methods.
Dr. Mousa Golalizadeh, Mr. Amir Razaghi,
Volume 24, Issue 1 (9-2019)
Abstract
The Principal Components Analysis is one of the popular exploratory approaches to reduce the dimension and to describe the main source of variation among data. Despite many benefits, it is encountered with some problems in multivariate analysis. Having outliers among data significantly influences the results of this method and it sounds a robust version of PCA is beneficial in this case. In addition, having moderate loadings in the final results makes the interpretation of principal components rather difficult. One can consider a version of sparse components in this case. We study a hybrid approach consisting of joint robust and sparse components and conduct some simulations to evaluate and compare it with other traditional methods. The proposed technique is implemented in a real-life example dealing with the crime rate in the USA.
Ms Monireh Maanavi, Dr Mahdi Roozbeh,
Volume 26, Issue 1 (12-2021)
Abstract
The method of least squares is a very simple, practical and useful approach for estimating regression coefficients of the linear models. This statistical method is used by users of different fields to provide the best unbiased linear estimator with the least variance. Unfortunately, this method will not have reliable output if outliers are present in the dataset, as the collapse point (estimator consistency criterion) of this method is 0% . It is therefore important to identify these observations. Until now, the various methods have been proposed to identify these observations. In this article, the proposed methods are reviewed and discussed in details. Finally, by presenting a simulation example, we examine each of the proposed methods.
Dr Mahdi Roozbeh, Ms mlihe Malekjafarian, Ms Monireh Maanavi,
Volume 26, Issue 2 (3-2022)
Abstract
The most important goal of statistical science is to analyze the real data of the world around us. If this information is analyzed accurately and correctly, the results will help us in many important decisions. Among the real data around us which its analysis is very important, is the water consumption data. Considering that Iran is located in a semi-arid climate area of the earth, it is necessary to take big steps for predicting and selecting the best and the most appropriate accurate models of water consumption, which is necessary for the macro-national decisions. But analyzing the real data is usually complicated. In the analysis of the real data set, we usually encounter with the problems of multicollinearity and outliers points. Robust methods are used for analyzing the datasets with outliers and ridge method is used for analyzing the data sets with multicollinearity. Also, the restriction on the models is resulted from using non-sample information in estimation of regression coefficients. In this paper, it is proceeded to model the water consumption data using robust stochastic restricted ridge approach and then, the performance of the proposed method is examined through a Monte Carlo simulation study.
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