TY - JOUR
T1 - An adaptive-to-model test for partially parametric single-index models
AU - Zhu, Xuehu
AU - Guo, Xu
AU - ZHU, Lixing
N1 - Lixing Zhu’s research was supported by a grant from the University Grants Council of Hong Kong, Hong Kong, China. Xu Guo’s research was supported by the Fundamental Research Funds for the Central Universities, No. NR2015001 and the Natural Science Foundation of Jiangsu Province, China, Grant No. BK20150732.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - Residual marked empirical process-based tests are commonly used in regression models. However, they suffer from data sparseness in high-dimensional space when there are many covariates. This paper has three purposes. First, we suggest a partial dimension reduction adaptive-to-model testing procedure that can be omnibus against general global alternative models although it fully use the dimension reduction structure under the null hypothesis. This feature is because that the procedure can automatically adapt to the null and alternative models, and thus greatly overcomes the dimensionality problem. Second, to achieve the above goal, we propose a ridge-type eigenvalue ratio estimate to automatically determine the number of linear combinations of the covariates under the null and alternative hypotheses. Third, a Monte-Carlo approximation to the sampling null distribution is suggested. Unlike existing bootstrap approximation methods, this gives an approximation as close to the sampling null distribution as possible by fully utilising the dimension reduction model structure under the null model. Simulation studies and real data analysis are then conducted to illustrate the performance of the new test and compare it with existing tests.
AB - Residual marked empirical process-based tests are commonly used in regression models. However, they suffer from data sparseness in high-dimensional space when there are many covariates. This paper has three purposes. First, we suggest a partial dimension reduction adaptive-to-model testing procedure that can be omnibus against general global alternative models although it fully use the dimension reduction structure under the null hypothesis. This feature is because that the procedure can automatically adapt to the null and alternative models, and thus greatly overcomes the dimensionality problem. Second, to achieve the above goal, we propose a ridge-type eigenvalue ratio estimate to automatically determine the number of linear combinations of the covariates under the null and alternative hypotheses. Third, a Monte-Carlo approximation to the sampling null distribution is suggested. Unlike existing bootstrap approximation methods, this gives an approximation as close to the sampling null distribution as possible by fully utilising the dimension reduction model structure under the null model. Simulation studies and real data analysis are then conducted to illustrate the performance of the new test and compare it with existing tests.
KW - Model checking
KW - Model-adaptation
KW - Partial sufficient dimension reduction
KW - Ridge-type eigenvalue ratio estimate
UR - http://www.scopus.com/inward/record.url?scp=84976498734&partnerID=8YFLogxK
U2 - 10.1007/s11222-016-9680-z
DO - 10.1007/s11222-016-9680-z
M3 - Journal article
AN - SCOPUS:84976498734
SN - 0960-3174
VL - 27
SP - 1193
EP - 1204
JO - Statistics and Computing
JF - Statistics and Computing
IS - 5
ER -