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master's thesis
Robusna regresija
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:050808
Lončar, Marko
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Lončar, M. (2021). Robusna regresija (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:050808

Lončar, Marko. "Robusna regresija." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:050808

Lončar, Marko. "Robusna regresija." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:050808

Lončar, M. (2021). 'Robusna regresija', Master's thesis, University of Zagreb, Faculty of Science, accessed 17 June 2024, https://urn.nsk.hr/urn:nbn:hr:217:050808

Lončar M. Robusna regresija [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2024 June 17] Available at: https://urn.nsk.hr/urn:nbn:hr:217:050808

M. Lončar, "Robusna regresija", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:050808

Metadata
TitleRobusna regresija
Title (english)Robust regression
AuthorMarko Lončar
MentorAzra Tafro (mentor)
Committee memberAzra Tafro (predsjednik povjerenstva)
Committee memberTomislav Pejković (član povjerenstva)
Committee memberIgor Ciganović (član povjerenstva)
Committee memberDijana Ilišević (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-09-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Robusne statističke metode osmišljene su kako bi se suzbili neki od problema koji se pojavljuju kod klasične statističke analize, kao što su odstupanja od pretpostavki modela ili neuobičajene vrijednosti (outlieri). Posebno, kod procjene parametara modela linearne regresije, standardna metoda najmanjih kvadrata veoma je osjetljiva na opažanja koja znatno odstupaju od ostalih. Nakon predstavljanja općih modela jednostavne linearne regresije, višestruke linearne regresije i metode najmanjih kvadrata, uvedene su dvije mjere robusnosti - breakdown vrijednost i funkcija utjecaja. Zatim su prikazane dvije robusne metode, metoda najmanjeg medijana kvadrata odstupanja i metoda najmanjih odrezanih kvadrata. Za te dvije metode dokazano je da postižu maksimalnu breakdown vrijednost. U konačnici, ilustrirani su primjeri na stvarnim podacima radi usporedbe klasične metode najmanjih kvadrata sa robusnim metodama. Primjeri su radeni u programskom jeziku R.
Abstract (english)
Robust statistical methods are designed to combat some of the problems that arise in classical statistical analysis, such as deviations from model assumptions and outliers. In particular, when estimating the parameters of a linear regression model, the standard least squares method is very sensitive to observations that deviate significantly from the others. After presenting the general forms of the simple linear regression model, multiple linear regression and the least squares method, two measures of robustness were introduced - the breakdown value and the influence function. Furthermore, two robust methods are presented, the least median squares method and the least trimmed squares method. These two methods have been shown to achieve a maximum breakdown value. Finally, examples with some real data and a comparison of the classical least squares method with robust methods are illustrated, using the programming language R.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:050808
Study programmeTitle: Finance and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-10-29 09:12:37