| dc.contributor.advisor |
Milošević, Bojana |
|
| dc.contributor.author |
Aleksić, Danijel |
|
| dc.date.accessioned |
2026-02-03T15:40:31Z |
|
| dc.date.available |
2026-02-03T15:40:31Z |
|
| dc.date.issued |
2026-01 |
|
| dc.identifier.uri |
http://hdl.handle.net/123456789/5781 |
|
| dc.description.abstract |
This dissertation addresses the problem of model specification testing in situa-
tions where data are incomplete, utilizing the existing theory of non-degenerate and weakly
degenerate U- and V-statistics. The first two chapters lay the theoretical groundwork by pre-
senting essential concepts related to U- and V-statistics and the general mathematical frame-
work of missing data analysis, which serve as the foundation for the new results developed in
subsequent chapters.
In Chapter 3, a novel test for assessing the missing completely at random (MCAR) assump-
tion is introduced. This test demonstrates improved control of the type I error rate and supe-
rior power performance compared to the main competitor across the majority of the simulated
scenarios examined.
Chapter 4 explores the application of Kendall’s test for independence in the presence of
MCAR data. It provides both theoretical insights and simulation-based comparisons of the
complete-case analysis and median imputation, pointing out their individual advantages and
drawbacks.
Chapter 5 focuses on testing for multivariate normality when data are incomplete. It rig-
orously establishes the validity of the complete-case approach under MCAR and proposes a
bootstrap method to approximate p -values when imputation is employed. Additionally, vari-
ous imputation techniques are evaluated with respect to their impact on the type I error and
the power of the test.
Finally, Chapter 6 adapts the energy-based two-sample test to handle missing data by intro-
ducing a weighted framework that makes full use of all available observations. Alongside some
theoretical developments, the chapter presents two distinct bootstrap algorithms for p -value
estimation under this approach. Additionally, the performance of several imputation methods
is examined in this context, and appropriate bootstrap algorithm is proposed for that setting. |
en_US |
| dc.description.provenance |
Submitted by Slavisha Milisavljevic (slavisha) on 2026-02-03T15:40:31Z
No. of bitstreams: 1
DanijelAleksicPhDThesis.pdf: 4605295 bytes, checksum: 7cb050554fff702e835de6dad1aca726 (MD5) |
en |
| dc.description.provenance |
Made available in DSpace on 2026-02-03T15:40:31Z (GMT). No. of bitstreams: 1
DanijelAleksicPhDThesis.pdf: 4605295 bytes, checksum: 7cb050554fff702e835de6dad1aca726 (MD5)
Previous issue date: 2026-01 |
en |
| dc.language.iso |
en |
en_US |
| dc.publisher |
Beograd |
en_US |
| dc.title |
U- AND V-STATISTICS FOR INCOMPLETE DATA AND THEIR APPLICATION TO MODEL SPECIFICATION TESTING |
en_US |
| mf.author.birth-date |
1998-09-25 |
|
| mf.author.birth-place |
Zvornik |
en_US |
| mf.author.birth-country |
Republika Srpska BiH |
en_US |
| mf.author.residence-state |
Srbija |
en_US |
| mf.author.citizenship |
Srpsko |
en_US |
| mf.author.nationality |
Srbin |
en_US |
| mf.subject.area |
Mathematics |
en_US |
| mf.subject.keywords |
missing data, model specification testing, tests of MCAR, independence testing, goodness-of-fit testing, two-sample testing, bootstrap. |
en_US |
| mf.subject.subarea |
Probability and Statistics |
en_US |
| mf.contributor.committee |
Cuparić, Marija |
|
| mf.contributor.committee |
Obradović, Marko |
|
| mf.contributor.committee |
Bastidis, Apostolos |
|
| mf.university.faculty |
Mathematical Faculty |
en_US |
| mf.document.pages |
105 |
en_US |
| mf.document.location |
Beograd |
en_US |
| mf.document.genealogy-project |
No |
en_US |
| mf.university |
Belgrade University |
en_US |