About: On the possibilistic approach to linear regression models involving uncertain, indeterminate or interval data

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We consider linear regression models where both input data (the observations of independent variables) and output data (the observations of the dependent variable) are affected by loss of information caused by uncertainty, indeterminacy, rounding or censoring. Instead of real-valued (crisp) data, only intervals are available. We study a possibilistic generalization of the least squares estimator, so called OLS-set for the interval model. Investigation of the OLS-set allows us to quantify whether the replacement of real-valued (crisp) data by interval values can have a significant impact on our knowledge of the value of the OLS estimator. We show that in the general case, very elementary questions about properties of the OLS-set are computationally intractable (assuming P - NP). We also focus on restricted versions of the general interval linear regression model to the crisp input case. Taking the advantage of the fact that in the crisp input - interval output model the OLS-set is a zonotope, we design both exact and approximate methods for its description. We also discuss special cases of the regression model, e.g. a model with repeated observations. We consider linear regression models where both input data (the observations of independent variables) and output data (the observations of the dependent variable) are affected by loss of information caused by uncertainty, indeterminacy, rounding or censoring. Instead of real-valued (crisp) data, only intervals are available. We study a possibilistic generalization of the least squares estimator, so called OLS-set for the interval model. Investigation of the OLS-set allows us to quantify whether the replacement of real-valued (crisp) data by interval values can have a significant impact on our knowledge of the value of the OLS estimator. We show that in the general case, very elementary questions about properties of the OLS-set are computationally intractable (assuming P - NP). We also focus on restricted versions of the general interval linear regression model to the crisp input case. Taking the advantage of the fact that in the crisp input - interval output model the OLS-set is a zonotope, we design both exact and approximate methods for its description. We also discuss special cases of the regression model, e.g. a model with repeated observations. (en)
Title	On the possibilistic approach to linear regression models involving uncertain, indeterminate or interval data On the possibilistic approach to linear regression models involving uncertain, indeterminate or interval data (en)
skos:prefLabel	On the possibilistic approach to linear regression models involving uncertain, indeterminate or interval data On the possibilistic approach to linear regression models involving uncertain, indeterminate or interval data (en)
skos:notation	RIV/00216208:11320/13:10159427!RIV14-GA0-11320___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GA13-10660S), P(GA201/09/0755), P(GAP403/12/1947), P(GBP402/12/G097)
http://linked.open...iv/cisloPeriodika	May
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Antoch, Jaromír Hladík, Milan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	93931
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/13:10159427
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Computational complexity; Possibilistic regression; Uncertain data; Interval data (en)
http://linked.open.../riv/klicoveSlovo	Interval data Computational complexity Possibilistic regression Uncertain data
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[BBAA266B5947]
http://linked.open...i/riv/nazevZdroje	Information Sciences
http://linked.open...in/vavai/riv/obor	BB
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Interval methods for optimization problems Models of Optimal Economic Decision Making under Instability, Uncertainty and Indeterminacy DYME-Dynamic Models in Economics Modelling nonhomogeneous time series
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	244
http://linked.open...iv/tvurceVysledku	Hladík, Milan Černý, Michal Antoch, Jaromír
http://linked.open...ain/vavai/riv/wos	000321479800002
issn	0020-0255
number of pages	22 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.ins.2013.04.035
http://localhost/t...ganizacniJednotka	11320

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