TY - JOUR
T1 - Empirical likelihood confidence regions of the parameters in a partially linear single-index model
AU - Xue, Liugen
AU - ZHU, Lixing
N1 - Funding Information:
supported by the Natural Science Foundation of Beijing City (Grant No. 1042002), Technology Development Plan Project of Beijing Education Committee (Grant No. KM200510005009) and the Special Grants of Beijing for Talents (Grant No. 20041D0501515). The second author was supported by a grant from the Research Grants Council of Hong Kong, Hong Kong (Grant No. HKU7060/04P).
PY - 2005/10
Y1 - 2005/10
N2 - In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.
AB - In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.
KW - Chi-square distribution
KW - Confidence region
KW - Coverage probability
KW - Empirical likelihood
KW - Partially linear single-index model
UR - http://www.scopus.com/inward/record.url?scp=27544488446&partnerID=8YFLogxK
U2 - 10.1360/04ys0139
DO - 10.1360/04ys0139
M3 - Article
AN - SCOPUS:27544488446
VL - 48
SP - 1333
EP - 1348
JO - Science in China, Series A: Mathematics, Physics, Astronomy
JF - Science in China, Series A: Mathematics, Physics, Astronomy
SN - 1006-9283
IS - 10
ER -