TY - JOUR
T1 - Polynomial spline estimation for partial functional linear regression models
AU - Zhou, Jianjun
AU - Chen, Zhao
AU - Peng, Qingyan
N1 - Funding Information:
The work was supported by National Nature Science Foundation of China (Grant Nos. 10961026, 11171293, 11225103, 11301464), the PH.D. Special Scientific Research Foundation of Chinese University (20115301110004), the Key Fund of Yunnan Province (Grant No. 2010CC003) and the Scientific Research Foundation of Yunnan Provincial Department of Education (No. 2013Y360). We are grateful to the referees and the editors for their constructive remarks that greatly improved the manuscript.
Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.
PY - 2016/9/1
Y1 - 2016/9/1
N2 - Because of its orthogonality, interpretability and best representation, functional principal component analysis approach has been extensively used to estimate the slope function in the functional linear model. However, as a very popular smooth technique in nonparametric/semiparametric regression, polynomial spline method has received little attention in the functional data case. In this paper, we propose the polynomial spline method to estimate a partial functional linear model. Some asymptotic results are established, including asymptotic normality for the parameter vector and the global rate of convergence for the slope function. Finally, we evaluate the performance of our estimation method by some simulation studies.
AB - Because of its orthogonality, interpretability and best representation, functional principal component analysis approach has been extensively used to estimate the slope function in the functional linear model. However, as a very popular smooth technique in nonparametric/semiparametric regression, polynomial spline method has received little attention in the functional data case. In this paper, we propose the polynomial spline method to estimate a partial functional linear model. Some asymptotic results are established, including asymptotic normality for the parameter vector and the global rate of convergence for the slope function. Finally, we evaluate the performance of our estimation method by some simulation studies.
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U2 - 10.1007/s00180-015-0636-0
DO - 10.1007/s00180-015-0636-0
M3 - Article
AN - SCOPUS:84952645489
SN - 0943-4062
VL - 31
SP - 1107
EP - 1129
JO - Computational Statistics
JF - Computational Statistics
IS - 3
ER -