Premium
Simpler proofs for functional sliced inverse regression
Author(s) -
Cui Xia,
Lian Heng
Publication year - 2018
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.200
Subject(s) - mathematical proof , functional principal component analysis , mathematics , regression , proper linear model , sliced inverse regression , regression analysis , linear regression , linear form , convergence (economics) , inverse , principal component analysis , polynomial regression , statistics , mathematical analysis , geometry , economics , economic growth
In this short communication, we demonstrate that functional sliced inverse regression obtains the same convergence rate as that presented in Hall, P & Horowitz, JL (2007), ‘Methodology and convergence rates for functional linear regression’, Annals of Statistics, 35(1), 70–91 for functional linear regression, both based on functional principal component analysis. This result is interesting because functional sliced inverse regression imposes far fewer structural constraints than functional linear regression, including an unknown link function. The two proofs provided emphasize the similarity between the two, and the proofs are thus much simpler than typically found in the literature. © 2018 John Wiley & Sons, Ltd.