Milan Hladík and Michal Černý. New approach to interval linear regression. In 24th Mini-EURO Conference On Continuous Optimization and Information-Based Technologies in The Financial Sector MEC EurOPT 2010. Selected Papers, pp. 167–171, Technika, Vilnius, 2010.
In interval regression analysis we aim at finding interval regression parameters that fit crisp or interval data. Diverse methods for this problem have been developed, however, many of them possess the property that some of the resulting regression parameters are crisp. This property is undesirable in a variety of applications. To overcome this drawback we propose a method motivated by tolerance analysis in linear systems. This method is not only computationally very cheap, but also yields intervals for regression parameters the widths of which are proportional to an in-advance given vector of parameters. For example, one choice of this vector allows to control relative tolerances and another leads to absolute tolerances. The tolerance quotient calculated by the method can also serve as a fitness measure of a given model. An example for a house price model is given.
@InProceedings{HlaCer2010a,
author = "Milan Hlad\'{\i}k and Michal {\v{C}}ern\'{y}",
editor = "R. Kas{\i}mbeyli and C. Din\c{c}er and S. {\"{O}}zpeynirci and L. Sakalauskas",
title = "New approach to interval linear regression",
booktitle = "{24th Mini-EURO Conference On Continuous Optimization and Information-Based Technologies in The Financial Sector MEC EurOPT 2010. Selected Papers}",
publisher = "Technika",
address = "Vilnius",
year = "2010",
pages = "167-171",
bib2html_dl_html = "http://www.vgtu.lt/leidiniai/leidykla/MEC_EurOPT_2010/005/0002.html",
abstract = "In interval regression analysis we aim at finding interval regression parameters that fit crisp or interval data. Diverse methods for this problem have been developed, however, many of them possess the property that some of the resulting regression parameters are crisp. This property is undesirable in a variety of applications. To overcome this drawback we propose a method motivated by tolerance analysis in linear systems. This method is not only computationally very cheap, but also yields intervals for regression parameters the widths of which are proportional to an in-advance given vector of parameters. For example, one choice of this vector allows to control relative tolerances and another leads to absolute tolerances. The tolerance quotient calculated by the method can also serve as a fitness measure of a given model. An example for a house price model is given.",
keywords = "possibilistic regression, fuzzy regression, interval regression",
}
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