TY - JOUR

T1 - Bi-additive models for extremes

AU - Antunes, Patrícia

AU - Ferreira, Sandra S.

AU - Ferreira, Dário

AU - Mexia, João T.

N1 - Publisher Copyright:
© 2022 Taylor & Francis Group, LLC.

PY - 2023

Y1 - 2023

N2 - To widen the application field of mixed models we introduce bi-additive models. These models are given by the sum of a fixed term (Formula presented.) and independent random effects terms (Formula presented.) Vectors (Formula presented.) will have (Formula presented.) components with (Formula presented.) th order cumulants (Formula presented.) We now consider the case in which the distributions of these components are distributed as Gumbel, Fréchet and Weibull types, estimating their cumulants and parameters. We then obtain (Formula presented.) confidence ellipsoids with [approximate] probability of containing realizations of the model. These ellipsoids can be used to, trough duality, test hypothesis on the fixed effects part (Formula presented.) of the models. Moreover matrices (Formula presented.) contain in their columns values of controlled variables and, for given values of the controlled variables, prediction intervals are obtained, containing future observations, with (Formula presented.) [approximate] probability. Three simulations studies, one for each distribution type, and an application to the Tagus river floods are included. We thus show how bi-additive models may be introduced in the important field of extreme value.

AB - To widen the application field of mixed models we introduce bi-additive models. These models are given by the sum of a fixed term (Formula presented.) and independent random effects terms (Formula presented.) Vectors (Formula presented.) will have (Formula presented.) components with (Formula presented.) th order cumulants (Formula presented.) We now consider the case in which the distributions of these components are distributed as Gumbel, Fréchet and Weibull types, estimating their cumulants and parameters. We then obtain (Formula presented.) confidence ellipsoids with [approximate] probability of containing realizations of the model. These ellipsoids can be used to, trough duality, test hypothesis on the fixed effects part (Formula presented.) of the models. Moreover matrices (Formula presented.) contain in their columns values of controlled variables and, for given values of the controlled variables, prediction intervals are obtained, containing future observations, with (Formula presented.) [approximate] probability. Three simulations studies, one for each distribution type, and an application to the Tagus river floods are included. We thus show how bi-additive models may be introduced in the important field of extreme value.

KW - Cumulants

KW - mixed models

KW - uniformly minimum variance unbiased estimator

UR - http://www.scopus.com/inward/record.url?scp=85126804875&partnerID=8YFLogxK

U2 - 10.1080/03610926.2022.2051053

DO - 10.1080/03610926.2022.2051053

M3 - Review article

AN - SCOPUS:85126804875

SN - 0361-0926

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

ER -