TY - JOUR
T1 - Faster convergence rate for functional linear regression in reproducing kernel Hilbert spaces
AU - Zhang, Fode
AU - Zhang, Weiping
AU - Li, Rui
AU - Lian, Heng
PY - 2020
Y1 - 2020
N2 - Functional linear regression is in the centre of research attention involving curves as units of observations. We focus on functional linear regression in the framework of reproducing kernel Hilbert spaces studied in Cai and Yuan [Minimax and adaptive prediction for functional linear regression. J Am Stat Assoc. 2012;107(499):1201–1216]. We extend their theoretical result establishing faster convergence rate under stronger conditions which is reduced to existing results when the stronger condition is removed. In particular, our result corroborates the expectation that with smoother functions the convergence rate of the estimator is faster.
AB - Functional linear regression is in the centre of research attention involving curves as units of observations. We focus on functional linear regression in the framework of reproducing kernel Hilbert spaces studied in Cai and Yuan [Minimax and adaptive prediction for functional linear regression. J Am Stat Assoc. 2012;107(499):1201–1216]. We extend their theoretical result establishing faster convergence rate under stronger conditions which is reduced to existing results when the stronger condition is removed. In particular, our result corroborates the expectation that with smoother functions the convergence rate of the estimator is faster.
KW - Convergence rate
KW - functional data
KW - reproducing kernel Hilbert space
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U2 - 10.1080/02331888.2019.1694931
DO - 10.1080/02331888.2019.1694931
M3 - 21_Publication in refereed journal
VL - 54
SP - 167
EP - 181
JO - Statistics
JF - Statistics
SN - 0233-1888
IS - 1
ER -