Kvantilna regresija

Rumenjak, Andrea (2014) Kvantilna regresija. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

Linear regression is a process in which we try to describe the dependent variable as a linear combination of one or more independent variables. It estimates the conditional expectation of the dependent variable for a given independent variable and it is shown as an affine function of the dependent variable. For this type of regression least squares method is efficient, but problems arise when we want to study the extreme values of some data or their quintiles. This is where quantile regression is useful. The quantile regression parameter represents the change in the dependent variable (response variable) in a specified quantile of a unit change in the independent variable (predictor variable). In quantile regression, the conditional median estimator is estimated by minimizing the symetrically weighted sum of absolute error (where the weight is equal to 0.5). The estimator for other conditional quantile function is estimated by minimizing the asymmetric weighted sum of absolute errors (where the weights are the functions of quintiles). Therefore, the quantile regression is robust to the presence of outliers as explained in this paper. Another advantage of quantile regression, shown in this paper, is equivariance that allows the quantile transformed random variables (transformed by strictly increasing affine functions) to be equal to the transformed quantiles of the original random variables, which is not the case with mathematical expectation. Therefore the interpretation of the model of quantile regression is simpler than in the method of least squares.

Item Type: Thesis (Diploma thesis)
Supervisor: Huzak, Miljenko
Date: 2014
Number of Pages: 38
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 09 Jul 2015 10:14
Last Modified: 09 Jul 2015 10:14
URI: http://digre.pmf.unizg.hr/id/eprint/4102

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