TY - JOUR
T1 - Model checks for functional linear regression models based on projected empirical processes
AU - Chen, Feifei
AU - Jiang, Qing
AU - Feng, Zhenghui
AU - ZHU, Lixing
N1 - Funding Information:
The authors thank the editor, co-editor and reviewers for their insightful suggestions that have helped to improve early version of this article. This work was supported by the National Natural Science Foundation of China [Grant Nos. 11871409 , 11671042 , and 11971064 ]; the Humanity and Social Science Youth Foundation of Ministry of Education of China [Grant No. 18YJC910006 ]; the Fundamental Research Funds for the Central Universities, China [Grant No. JBK1805004 ]; the Joint Lab of Data Science and Business Intelligence at Southwestern University of Finance and Economics, China ; and a grant from the University Grants Council of Hong Kong . Appendix A.1
Funding Information:
The authors thank the editor, co-editor and reviewers for their insightful suggestions that have helped to improve early version of this article. This work was supported by the National Natural Science Foundation of China [Grant Nos. 11871409, 11671042, and 11971064]; the Humanity and Social Science Youth Foundation of Ministry of Education of China [Grant No. 18YJC910006]; the Fundamental Research Funds for the Central Universities, China [Grant No. JBK1805004]; the Joint Lab of Data Science and Business Intelligence at Southwestern University of Finance and Economics, China; and a grant from the University Grants Council of Hong Kong.
PY - 2020/4
Y1 - 2020/4
N2 - The goodness-of-fit testing for functional linear regression models with functional responses is studied. A residual-marked empirical process-based test is proposed. The test is projection-based, which can well circumvent the curse of dimensionality. The test is omnibus against any global alternative hypothesis as it integrates over all projection directions in the unit ball. The weak convergence of the test statistic under the null hypothesis is derived and it is shown that the proposed test can detect the local alternative hypotheses distinct from the null hypothesis at the fastest possible rate of order O(n−1∕2). To reduce computational burden for critical value determination, a nonparametric Monte Carlo method is used, and simulation studies show the good performance of the proposed method in various scenarios. An ergonomics data set is analyzed for illustration.
AB - The goodness-of-fit testing for functional linear regression models with functional responses is studied. A residual-marked empirical process-based test is proposed. The test is projection-based, which can well circumvent the curse of dimensionality. The test is omnibus against any global alternative hypothesis as it integrates over all projection directions in the unit ball. The weak convergence of the test statistic under the null hypothesis is derived and it is shown that the proposed test can detect the local alternative hypotheses distinct from the null hypothesis at the fastest possible rate of order O(n−1∕2). To reduce computational burden for critical value determination, a nonparametric Monte Carlo method is used, and simulation studies show the good performance of the proposed method in various scenarios. An ergonomics data set is analyzed for illustration.
KW - Functional linear models
KW - Model checking
KW - Projected empirical processes
KW - Residual-marked
UR - http://www.scopus.com/inward/record.url?scp=85076552903&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2019.106897
DO - 10.1016/j.csda.2019.106897
M3 - Article
AN - SCOPUS:85076552903
SN - 0167-9473
VL - 144
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
M1 - 106897
ER -