Bootstrap metoda u prilagodbi linearnog regresijskog modela

master's thesis

• Author: Bernarda Tomić
• Mentor: Miljenko Huzak (mentor)
• Committee member: Miljenko Huzak (predsjednik povjerenstva)
• Committee member: Maja Starčević (član povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-02-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Cilj ovog diplomskog rada je dati kratki pregled bootstrap metode, posebice za linearni regresijski model. Metoda se koristi za procjenu nesigurnosti. Korisna je kod zaključivanja koje se bazira na kompleksnim postupcima za koje su teoretski rezultati nedostupni, nisu primjenjivi na dostupnim uzorcima zbog njihove veličine ili pak kada je dostupni uzorak mali. Također je primjenjiva kada nismo sigurni koji model primijeniti ili kada jednostavno trebamo ’quick and dirty’ analizu. Uvod sadrži kratki opis metoda ponovljenog uzorkovanja (jaccknife, bootstrap, kros - validacija i randomizacijski test), glavnu ideju bootstrapa i motivacijski primjer (procjena modificirane sredine populacije). U prvom poglavlju detaljnije se prikazani neparametarski, parametarski i poluparametarski bootstrap s odgovarajućim primjerima. Argumentirane su opravdanost bootstrapa i mogućnost smanjenja pogreške tijekom primjene metode. U drugom poglavlju pokazana je primjena metode na primjeru linearnog regresijskog modela. Opisane su metode ponovljenog uzorkovanja parova i ponovljenog uzorkovanja pogrešaka. Dani su također primjeri. Na kraju je sažeto kada je bootstrap primjenjiv, a kada podbacuje.

Abstract (english)

The goal of this master’s thesis is to give an introduction to the bootstrap (bootstrapping), especially for the linear regression model. The method is used for assessing uncertainty. It is useful when inference is to be based on a complex procedure for which theoretical results are unavailable or not useful for the sample sizes met in practice, where a standard model is suspect but it is unclear with what to replace it, or when ’quick and dirty’ answer is required. It can also be used to verify the usefulness of standard approximations for parametric models, and to improve them if they seem to give inadequate inferences. In the introduction you can find the description of the resampling methods (the jacckinife, the bootstrap, cross-validation and randomization test), the main principle of the bootstrap and a motivation example (estimate of the trimmed mean of the population). In the first chapter parametric, nonparametric and semiparametric bootstrap are explained with the given examples. The validity of the method and reducing error are argumented. In the second chapter the application on the regression model is shown. The methods of resampling the residuals and resampling the errors are described. The methods the examples are also given. In the end there is a conclusion about when to use bootstrap and when it is not recommended.

• Keywords: bootstrap metoda; linearni regresijski model; procjena nesigurnosti
• Keywords (english): bootstrap; linear regression model; assessing uncertainty
• Language: croatian
• URN:NBN: urn:nbn:hr:217:680599
• 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: 2019-02-15 08:43:23