Neparametarska regresija

master's thesis

• Title (english): Non-parametric regression
• Author: Tin Sertić
• Mentor: Azra Tafro (mentor)
• Committee member: Azra Tafro (predsjednik povjerenstva)
• Committee member: Vjekoslav Kovač (član povjerenstva)
• Committee member: Ozren Perše (član povjerenstva)
• Committee member: Marko Horvat (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-11-30, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu predstavili smo metode neparametarske regresije kao alternativu poznatijim metodama parametarske regresije. Za razliku od metoda parametarske regresije, koje nastoje procijeniti procjenitelja nekog određenog oblika s konačnim brojem parametara, neparametarske metode nastoje prvo procijeniti oblik funkcije (ili broj parametara) i onda prilagoditi procjenitelja određenom obliku. Kako bismo procijenili oblik funkcije, prezentirali smo pomoćne metode leave-one-out i generalizirane unakrsne validacije. Nakon toga, predstavili smo metodu lokalnih prosjeka, metodu procjene jezgrom i metodu lokalne linearne regresije kao glavne predstavnike klase linearnih procjenitelja. Predstavljene metode ilustrirali smo pojedinačno i zajedno na nekoliko primjera u programskom jeziku R kako bismo čitatelju uz teoretsku osnovu, pružili i praktično znanje iz obrađenog područja.

Abstract (english)

In this master’s thesis, we presented nonparametric regression methods as an alternative to more well-known parametric regression methods. Unlike parametric regression methods, which aim to estimate a predictor of a specific form with a finite number of parameters, nonparametric methods first seek to estimate the shape of the function (or the number of parameters) and then adapt the estimator to a specific form. To estimate the shape of the function, we introduced auxiliary methods such as leaveone- out and generalized cross-validation. Subsequently, we introduced the local averaging method, kernel estimation method, and local linear regression method as key representatives of the class of linear smoothers. We illustrated these methods individually and collectively on several examples in the R programming language to provide the reader with both theoretical foundations and practical knowledge in the covered area.

• Keywords: metode parametarske regresije; leave-one-out; generalizirana unakrsna validacija; metoda lokalnih prosjeka; metoda procjene jezgrom; metoda lokalne linearne regresije; programskom jeziku R
• Keywords (english): parametric regression methods; leaveone- out; local averaging method; kernel estimation method; local linear regression method; R programming language
• Language: croatian
• URN:NBN: urn:nbn:hr:217:162983
• Study programme: Title: Financial and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-02-13 08:18:42