Robusna regresija

master's thesis

• Title (english): Robust regression
• Author: Marko Lončar
• Mentor: Azra Tafro (mentor)
• Committee member: Azra Tafro (predsjednik povjerenstva)
• Committee member: Tomislav Pejković (član povjerenstva)
• Committee member: Igor Ciganović (član povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-09-21, 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: klasična statistička analiza; outlieri; modeli linearne regresije; breakdown vrijednost; funkcija utjecaja; metoda najmanjeg medijana kvadrata odstupanja; metoda najmanjih odrezanih kvadrata
• Keywords (english): classical statistical analysis; outliers; breakdown value; the influence function; least median squares method; least trimmed squares method
• Language: croatian
• URN:NBN: urn:nbn:hr:217:050808
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-10-29 09:12:37