TY - JOUR
T1 - Estimation for biased partial linear single index models
AU - Lu, Jun
AU - Zhu, Xuehu
AU - Lin, Lu
AU - ZHU, Lixing
N1 - Funding Information:
Jun Lu research was supported by National Natural Science Foundation of China (No. 71671165 ), Philosophy and Social Science Planning Projects of Zhejiang (No. 17NDJC211YB ), First Class Discipline of Zhejiang - A (Zhejiang Gongshang University-Statistics) . Xuehu Zhu research was supported by National Natural Science Foundation of China (No. 11601415 , No. 61877049 ), China Postdoctoral Science Foundation (No. 2016M590934 , No. 2017T100731 ) and was supported by “ the Fundamental Research Funds for the Central Universities ”. Lu Lin research was supported by National Natural Science Foundation of China (No. 11571204 ). Lixing Zhu research was supported by a grant from the University Grants Council of Hong Kong, Hong Kong, China and by National Natural Science Foundation of China (No. 11671042 ). The authors thank the editor, the associate editor and anonymous referees for their constructive comments and suggestions which led to a substantial improvement of an early manuscript.
PY - 2019/11
Y1 - 2019/11
N2 - In this paper, we propose a novel method to consistently estimate, at the root-n rate, the coefficient parameters in a biased partial linear single-index model whose error term does not have zero conditional expectation. To achieve this purpose, we first transfer the model to a pro forma linear model and then introduce an artificial variable into a linear bias correction model. Based on the bias correction model, the parameters can then be consistently estimated by the linear least squares method. Both numerical studies and real data analyses are conducted to show the effectiveness of the proposed estimation procedure.
AB - In this paper, we propose a novel method to consistently estimate, at the root-n rate, the coefficient parameters in a biased partial linear single-index model whose error term does not have zero conditional expectation. To achieve this purpose, we first transfer the model to a pro forma linear model and then introduce an artificial variable into a linear bias correction model. Based on the bias correction model, the parameters can then be consistently estimated by the linear least squares method. Both numerical studies and real data analyses are conducted to show the effectiveness of the proposed estimation procedure.
KW - Artificial variable construction
KW - Bias-corrected model
KW - Estimation consistency
KW - Partial linear single index model
UR - http://www.scopus.com/inward/record.url?scp=85065094453&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2019.03.006
DO - 10.1016/j.csda.2019.03.006
M3 - Article
AN - SCOPUS:85065094453
SN - 0167-9473
VL - 139
SP - 1
EP - 13
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
ER -