TY - JOUR
T1 - Generalized functional additive models in reproducing kernel Hilbert spaces
AU - Peng, Ling
AU - Liu, Xiao Hui
AU - Rizk, Zeinab
AU - Zhou, Yi Wen
AU - Lian, Heng
PY - 2026
Y1 - 2026
N2 - This paper introduces a generalized functional additive model (G-FAM) that accommodates responses generated from various distributions within the exponential family, including normal, binomial, and Poisson distributions. We minimize a penalized negative log-likelihood function within the reproducing kernel Hilbert space (RKHS) framework to estimate the unknown functional coefficients. We further establish the optimal convergence rate of the proposed estimator under mild conditions. The empirical performance of our method is demonstrated through simulation studies and an application to real data. This paper introduces a generalized functional additive model (G-FAM) that accommodates responses generated from various distributions within the exponential family, including normal, binomial, and Poisson distributions. We minimize a penalized negative log-likelihood function within the reproducing kernel Hilbert space (RKHS) framework to estimate the unknown functional coefficients. We further establish the optimal convergence rate of the proposed estimator under mild conditions. The empirical performance of our method is demonstrated through simulation studies and an application to real data. © 2026 International Press, Inc.. All rights reserved.
AB - This paper introduces a generalized functional additive model (G-FAM) that accommodates responses generated from various distributions within the exponential family, including normal, binomial, and Poisson distributions. We minimize a penalized negative log-likelihood function within the reproducing kernel Hilbert space (RKHS) framework to estimate the unknown functional coefficients. We further establish the optimal convergence rate of the proposed estimator under mild conditions. The empirical performance of our method is demonstrated through simulation studies and an application to real data. This paper introduces a generalized functional additive model (G-FAM) that accommodates responses generated from various distributions within the exponential family, including normal, binomial, and Poisson distributions. We minimize a penalized negative log-likelihood function within the reproducing kernel Hilbert space (RKHS) framework to estimate the unknown functional coefficients. We further establish the optimal convergence rate of the proposed estimator under mild conditions. The empirical performance of our method is demonstrated through simulation studies and an application to real data. © 2026 International Press, Inc.. All rights reserved.
KW - Convergence rate
KW - Generalized functional additive models
KW - Negative log-likelihood
KW - Reproducing kernel Hilbert space
UR - http://www.scopus.com/inward/record.url?scp=105028742789&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-105028742789&origin=recordpage
U2 - 10.4310/SII.260107225454
DO - 10.4310/SII.260107225454
M3 - RGC 21 - Publication in refereed journal
SN - 1938-7989
VL - 19
SP - 71
EP - 84
JO - Statistics and Its Interface
JF - Statistics and Its Interface
IS - 1
ER -