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master's thesis
Martingalne procjeniteljske funkcije
2023. urn:nbn:hr:126:245857
Ujić, Nataša
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

Cite this document

Ujić, N. (2023). Martingalne procjeniteljske funkcije (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:245857

Ujić, Nataša. "Martingalne procjeniteljske funkcije." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:245857

Ujić, Nataša. "Martingalne procjeniteljske funkcije." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:245857

Ujić, N. (2023). 'Martingalne procjeniteljske funkcije', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 24 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:245857

Ujić N. Martingalne procjeniteljske funkcije [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2023 [cited 2024 December 24] Available at: https://urn.nsk.hr/urn:nbn:hr:126:245857

N. Ujić, "Martingalne procjeniteljske funkcije", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:126:245857

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Metadata
TitleMartingalne procjeniteljske funkcije
Title (english)Martingale Estimating Functions
AuthorNataša Ujić
MentorNenad Šuvak (mentor)
Committee memberDanijel Grahovac (predsjednik povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
Committee memberIvan Papić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2023-10-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
U ovome radu prvo su definirana neka osnovna svojstva procjenitelja te pojmovi vezani za slučajne procese. Ukratko su opisani Itôv stohastički integral, stohastičke diferencijalne jednadžbe te difuzije. Nakon toga, dane su osnovne informacije o procjeniteljskim funkcijama kao jednom od načina procjene parametara. Specifičnu klasu procjeniteljskih funkcija čine martingalne procjeniteljske funkcije, kojima je posvećen glavni dio ovoga rada. Optimalnost u smislu Godambea prvo je opisana u generalnom slučaju procjeniteljskih funkcija, a zatim je, uz optimalnost u smislu Heydea, komentirana i u slučaju martingalnih procjeniteljskih funkcija. Navedeno je nekoliko tvrdnji koje objašnjavaju normalnu asimptotsku distribuiranost procjenitelja dobivenih pomoću martingalnih procjeniteljskih funkcija i komentirana je njihova egzistencija te jedinstvenost. Štoviše, navedena je aproksimacija skor funkcije i definiran izraz za optimalnu težinsku matricu koja određuje težinu pojedinih funkcija korištenih u aproksimaciji. Na kraju rada, komentiran je primjer u kojemu se martingalna procjeniteljska funkcija može eksplicitno izraziti pomoću svojstvenih funkcija te su analizirane vrijednosti procjenitelja dobivenih simulacijama.
Abstract (english)
In this paper, some basic properties of estimators and terms related to stochastic processes are firstly defined. Itô’s stochastic integral, stochastic differential equations and diffusion process are briefly described. After that, basic information about estimating functions as one of the ways of estimating parameters are given. A specific class of estimating functions are martingale estimating functions, which the main part of this paper is dedicated to. Optimality in the sense of Godambe was first described in the general case of estimating functions, and then, along with optimality in the sense of Heyde, it was also commented on in the case of martingale estimating functions. Several statements explaining the normal asymptotic distribution of estimators obtained using martingale estimating functions are stated and their existence and uniqueness are commented on. Moreover, the approximation of the score function is specified and the expression for the optimal weight matrix that determines the weight of individual functions used in the approximation is defined. At the end of the paper, an example in which the martingale estimator function can be explicitly expressed using eigenfunctions was commented, and the values of estimators obtained by simulations were analyzed.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:245857
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical 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 on2023-11-10 10:12:43