TY  - JOUR
AU  - Stojanović, Vladica
AU  - Ljajko, Eugen
AU  - Tošić, Marina
PY  - 2023
UR  - https://jakov.kpu.edu.rs/handle/123456789/1645
AB  - This manuscript deals with a parameter estimation of a non-negative integer-valued (NNIV) time series based on the so-called probability generating function (PGF) method. The theoretical background of the PGF estimation technique for a very general, stationary class of NNIV time series is described, as well as the asymptotic properties of the obtained estimates. After that, a particular emphasis is given to PGF estimators of independent identical distributed (IID) and integer-valued non-negative autoregressive (INAR) series. A Monte Carlo study of the thus obtained PGF estimates, based on a numerical integration of the appropriate objective function, is also presented. For this purpose, numerical quadrature formulas were computed using Gegenbauer orthogonal polynomials. Finally, the application of the PGF estimators in the dynamic analysis of some actual data is given.
PB  - Basel : MDPI
T2  - Axioms
T1  - Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions
VL  - 12
IS  - 2
SP  - 112
DO  - 10.3390/axioms12020112
ER  - 

@article{
author = "Stojanović, Vladica and Ljajko, Eugen and Tošić, Marina",
year = "2023",
abstract = "This manuscript deals with a parameter estimation of a non-negative integer-valued (NNIV) time series based on the so-called probability generating function (PGF) method. The theoretical background of the PGF estimation technique for a very general, stationary class of NNIV time series is described, as well as the asymptotic properties of the obtained estimates. After that, a particular emphasis is given to PGF estimators of independent identical distributed (IID) and integer-valued non-negative autoregressive (INAR) series. A Monte Carlo study of the thus obtained PGF estimates, based on a numerical integration of the appropriate objective function, is also presented. For this purpose, numerical quadrature formulas were computed using Gegenbauer orthogonal polynomials. Finally, the application of the PGF estimators in the dynamic analysis of some actual data is given.",
publisher = "Basel : MDPI",
journal = "Axioms",
title = "Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions",
volume = "12",
number = "2",
pages = "112",
doi = "10.3390/axioms12020112"
}

Stojanović, V., Ljajko, E.,& Tošić, M.. (2023). Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions. in Axioms
Basel : MDPI., 12(2), 112.
https://doi.org/10.3390/axioms12020112

Stojanović V, Ljajko E, Tošić M. Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions. in Axioms. 2023;12(2):112.
doi:10.3390/axioms12020112 .

Stojanović, Vladica, Ljajko, Eugen, Tošić, Marina, "Parameters Estimation in Non-Negative Integer-Valued Time Series: Approach Based on Probability Generating Functions" in Axioms, 12, no. 2 (2023):112,
https://doi.org/10.3390/axioms12020112 . .

TY  - JOUR
AU  - Tošić, Marina
AU  - Ljajko, Eugen
AU  - Kontrec, Nataša
AU  - Stojanović, Vladica
PY  - 2020
UR  - https://jakov.kpu.edu.rs/handle/123456789/1635
AB  - Baksalary et al. (Linear Algebra Appl., doi:10.1016/j.laa.2004.02.025, 2004) investigated the invertibility of a linear combination of idempotent matrices. This result was improved by Koliha et al. (Linear Algebra Appl., doi:10.1016/j.laa.2006.01.011, 2006) by showing that the rank of a linear combination of two idempotents is constant. In this paper, we consider similar problems for k-potent matrices. We study the rank and the nullity of a linear combination of two commuting k-potent matrices. Furthermore, the problem of the nonsingularity of linear combinations of two or three k-potent matrices is considered under some conditions. In these situations, we derive explicit formulae of their inverses.
PB  - Basel : MDPI
T2  - Mathematics
T1  - The Nullity, Rank, and Invertibility of Linear Combinations of k-Potent Matrices
VL  - 8
IS  - 12
SP  - 2147
DO  - 10.3390/math8122147
ER  - 

@article{
author = "Tošić, Marina and Ljajko, Eugen and Kontrec, Nataša and Stojanović, Vladica",
year = "2020",
abstract = "Baksalary et al. (Linear Algebra Appl., doi:10.1016/j.laa.2004.02.025, 2004) investigated the invertibility of a linear combination of idempotent matrices. This result was improved by Koliha et al. (Linear Algebra Appl., doi:10.1016/j.laa.2006.01.011, 2006) by showing that the rank of a linear combination of two idempotents is constant. In this paper, we consider similar problems for k-potent matrices. We study the rank and the nullity of a linear combination of two commuting k-potent matrices. Furthermore, the problem of the nonsingularity of linear combinations of two or three k-potent matrices is considered under some conditions. In these situations, we derive explicit formulae of their inverses.",
publisher = "Basel : MDPI",
journal = "Mathematics",
title = "The Nullity, Rank, and Invertibility of Linear Combinations of k-Potent Matrices",
volume = "8",
number = "12",
pages = "2147",
doi = "10.3390/math8122147"
}

Tošić, M., Ljajko, E., Kontrec, N.,& Stojanović, V.. (2020). The Nullity, Rank, and Invertibility of Linear Combinations of k-Potent Matrices. in Mathematics
Basel : MDPI., 8(12), 2147.
https://doi.org/10.3390/math8122147

Tošić M, Ljajko E, Kontrec N, Stojanović V. The Nullity, Rank, and Invertibility of Linear Combinations of k-Potent Matrices. in Mathematics. 2020;8(12):2147.
doi:10.3390/math8122147 .

Tošić, Marina, Ljajko, Eugen, Kontrec, Nataša, Stojanović, Vladica, "The Nullity, Rank, and Invertibility of Linear Combinations of k-Potent Matrices" in Mathematics, 8, no. 12 (2020):2147,
https://doi.org/10.3390/math8122147 . .