TY - JOUR
T1 - Bias-corrected empirical likelihood in a multi-link semiparametric model
AU - ZHU, Lixing
AU - Lin, Lu
AU - Cui, Xia
AU - Li, Gaorong
N1 - Lu Lin’s research was supported by NBRP (973 Program 2007CB814901) of China, NNSF project (10771123) of China, RFDP (20070422034) of China, NSF projects (Y2006A13 and Q2007A05) of Shandong Province of China. Lixing Zhu’s research was supported by a grant from Research Grants Council of Hong Kong and a FRG grant from Hong Kong Baptist University. Gaorong Li’s research was supported by China Postdoctoral Science Foundation Funded Project (20080430633) and Shanghai Postdoctoral Scientific Program (08R214121).
PY - 2010/4
Y1 - 2010/4
N2 - In this paper, we investigate the empirical likelihood for constructing a confidence region of the parameter of interest in a multi-link semiparametric model when an infinite-dimensional nuisance parameter exists. The new model covers the commonly used varying coefficient, generalized linear, single-index, multi-index, hazard regression models and their generalizations, as its special cases. Because of the existence of the infinite-dimensional nuisance parameter, the classical empirical likelihood with plug-in estimation cannot be asymptotically distribution-free, and the existing bias correction is not extendable to handle such a general model. We then propose a link-based correction approach to solve this problem. This approach gives a general rule of bias correction via an inner link, and consists of two parts. For the model whose estimating equation contains the score functions that are easy to estimate, we use a centering for the scores to correct the bias; for the model of which the score functions are of complex structure, a bias-correction procedure using simpler functions instead of the scores is given without loss of asymptotic efficiency. The resulting empirical likelihood shares the desired features: it has a chi-square limit and, under-smoothing technique, high order kernel and parameter estimation are not needed. Simulation studies are carried out to examine the performance of the new method.
AB - In this paper, we investigate the empirical likelihood for constructing a confidence region of the parameter of interest in a multi-link semiparametric model when an infinite-dimensional nuisance parameter exists. The new model covers the commonly used varying coefficient, generalized linear, single-index, multi-index, hazard regression models and their generalizations, as its special cases. Because of the existence of the infinite-dimensional nuisance parameter, the classical empirical likelihood with plug-in estimation cannot be asymptotically distribution-free, and the existing bias correction is not extendable to handle such a general model. We then propose a link-based correction approach to solve this problem. This approach gives a general rule of bias correction via an inner link, and consists of two parts. For the model whose estimating equation contains the score functions that are easy to estimate, we use a centering for the scores to correct the bias; for the model of which the score functions are of complex structure, a bias-correction procedure using simpler functions instead of the scores is given without loss of asymptotic efficiency. The resulting empirical likelihood shares the desired features: it has a chi-square limit and, under-smoothing technique, high order kernel and parameter estimation are not needed. Simulation studies are carried out to examine the performance of the new method.
KW - Bias correction
KW - Chi-square distribution
KW - Confidence region
KW - Empirical likelihood ratio
KW - Multi-link semiparametric model
KW - Test statistic
UR - http://www.scopus.com/inward/record.url?scp=74449093887&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2009.08.009
DO - 10.1016/j.jmva.2009.08.009
M3 - Journal article
AN - SCOPUS:74449093887
SN - 0047-259X
VL - 101
SP - 850
EP - 868
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - 4
ER -