TY - JOUR
T1 - Simultaneous confidence band and hypothesis test in generalised varying-coefficient models
AU - Zhang, Wenyang
AU - Peng, Heng
N1 - Funding Information:
We thank the associate editor and the referees for their very helpful comments. Heng Peng’s research is supported by CERG Grants of Hong Kong Research Grant Council ( HKBU 201707 and HKBU 201809 ), FRG Grant from Hong Kong Baptist University FRG/08-09/II-33 , and a Grant from National Nature Science Foundation of China ( NNSF 10871054 ).
PY - 2010/8
Y1 - 2010/8
N2 - Generalised varying-coefficient models (GVC) are very important models. There are a considerable number of literature addressing these models. However, most of the existing literature are devoted to the estimation procedure. In this paper, we systematically investigate the statistical inference for GVC, which includes confidence band as well as hypothesis test. We establish the asymptotic distribution of the maximum discrepancy between the estimated functional coefficient and the true functional coefficient. We compare different approaches for the construction of confidence band and hypothesis test. Finally, the proposed statistical inference methods are used to analyse the data from China about contraceptive use there, which leads to some interesting findings.
AB - Generalised varying-coefficient models (GVC) are very important models. There are a considerable number of literature addressing these models. However, most of the existing literature are devoted to the estimation procedure. In this paper, we systematically investigate the statistical inference for GVC, which includes confidence band as well as hypothesis test. We establish the asymptotic distribution of the maximum discrepancy between the estimated functional coefficient and the true functional coefficient. We compare different approaches for the construction of confidence band and hypothesis test. Finally, the proposed statistical inference methods are used to analyse the data from China about contraceptive use there, which leads to some interesting findings.
KW - Generalised likelihood ratio test
KW - Generalised varying-coefficient models
KW - Hypothesis test
KW - Local linear modelling
KW - Simultaneous confidence band
UR - http://www.scopus.com/inward/record.url?scp=77951994459&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2010.03.003
DO - 10.1016/j.jmva.2010.03.003
M3 - Journal article
AN - SCOPUS:77951994459
SN - 0047-259X
VL - 101
SP - 1656
EP - 1680
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - 7
ER -