TY - JOUR
T1 - Smoothed rank correlation of the linear transformation regression model
AU - Lin, Huazhen
AU - PENG, Heng
N1 - Funding Information:
Peng’s research was supported by CERG grants from the Hong Kong Research Grants Council (HKBU 201610 , HKBU 201809 and HKBU 202012 ), FRG grants from Hong Kong Baptist University ( FRG/10-11/024 and FRG/11-12/130 ).
Funding Information:
Lin’s research was supported by the National Natural Science Funds for Distinguished Young Scholar (No. 11125104 ), the National Natural Science Foundation of China (No. 11071197 ) and Program for New Century Excellent Talents in University.
PY - 2013/1
Y1 - 2013/1
N2 - The maximum rank correlation (MRC) approach is the most common method used in the literature to estimate the regression coefficients in the semiparametric linear transformation regression model. However, the objective function Gn(β) in the MRC approach is not continuous. The optimization of Gn(β) requires an extensive search for which the computational cost grows in the order of nd, where d is the dimension of X. Given the lack of smoothing, issues related to variable selection, the variance estimate and other inferences by MRC are not well developed in the model. In this paper, we combine the concept underlying the penalized method, rank correlation and smoothing technique and propose a nonconcave penalized smoothed rank correlation method to select variables and estimate parameters for the semiparametric linear transformation model. The proposed estimator is computationally simple, n1 2-consistent and asymptotically normal. A sandwich formula is proposed to estimate the variances of the proposed estimates. We also illustrate the usefulness of the methodology with real data from a body fat prediction study.
AB - The maximum rank correlation (MRC) approach is the most common method used in the literature to estimate the regression coefficients in the semiparametric linear transformation regression model. However, the objective function Gn(β) in the MRC approach is not continuous. The optimization of Gn(β) requires an extensive search for which the computational cost grows in the order of nd, where d is the dimension of X. Given the lack of smoothing, issues related to variable selection, the variance estimate and other inferences by MRC are not well developed in the model. In this paper, we combine the concept underlying the penalized method, rank correlation and smoothing technique and propose a nonconcave penalized smoothed rank correlation method to select variables and estimate parameters for the semiparametric linear transformation model. The proposed estimator is computationally simple, n1 2-consistent and asymptotically normal. A sandwich formula is proposed to estimate the variances of the proposed estimates. We also illustrate the usefulness of the methodology with real data from a body fat prediction study.
KW - MRC
KW - Semiparametric transformation model
KW - Variable selection
KW - Variance estimation
UR - http://www.scopus.com/inward/record.url?scp=84865410268&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2012.07.012
DO - 10.1016/j.csda.2012.07.012
M3 - Journal article
AN - SCOPUS:84865410268
SN - 0167-9473
VL - 57
SP - 615
EP - 630
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
IS - 1
ER -