TY - JOUR
T1 - Matching Kollo measures
AU - Alexander, Carol
AU - Wei, Wei
AU - Chen, Xi
PY - 2023/8/9
Y1 - 2023/8/9
N2 - We motivate the advantages of using the Kollo measures, relative to other types of third and fourth moments of multivariate systems, and explore their Monte Carlo simulation and bootstrapping errors. Then we derive necessary and sufficient conditions for simultaneously matching any given mean vector, covariance matrix, Kollo skewness, and Kollo kurtosis. The specification of a suitable orthonormal basis greatly simplifies these moment-matching conditions. We offer semi-closed-form solutions to increase computational efficiency. In this respect, we compare our approach to two competing methods, which anyway can only match Kollo skewness and not the kurtosis at the same time. Ours is the first method for exactly matching all four multivariate moments simultaneously.
AB - We motivate the advantages of using the Kollo measures, relative to other types of third and fourth moments of multivariate systems, and explore their Monte Carlo simulation and bootstrapping errors. Then we derive necessary and sufficient conditions for simultaneously matching any given mean vector, covariance matrix, Kollo skewness, and Kollo kurtosis. The specification of a suitable orthonormal basis greatly simplifies these moment-matching conditions. We offer semi-closed-form solutions to increase computational efficiency. In this respect, we compare our approach to two competing methods, which anyway can only match Kollo skewness and not the kurtosis at the same time. Ours is the first method for exactly matching all four multivariate moments simultaneously.
KW - multivariate simulation
KW - moment matching
KW - Kollo Measure
U2 - 10.1080/01605682.2023.2240847
DO - 10.1080/01605682.2023.2240847
M3 - Article (Academic Journal)
SN - 1476-9360
JO - Journal of the Operational Research Society
JF - Journal of the Operational Research Society
ER -