scholarly journals B-spline estimation in varying coefficient models with correlated errors

2021 ◽  
Vol 7 (3) ◽  
pp. 3509-3523
Author(s):  
Yanping Liu ◽  
◽  
Juliang Yin
Keyword(s):  
Convergence Rates ◽  
Regression Function ◽  
Estimation Methods ◽  
Varying Coefficient Model ◽  
Correlated Errors ◽  
Computationally Efficient ◽  
Smooth Functions ◽  
B Spline ◽  
Varying Coefficient ◽  
Spline Estimation

<abstract><p>The varying coefficient model assumes that the regression function depends linearly on some regressors, and that the regression coefficients are smooth functions of other predictor variables. It provides an appreciable flexibility in capturing the underlying dynamics in data and avoids the so-called "curse of dimensionality" in analyzing complex and multivariate nonlinear structures. Existing estimation methods usually assume that the errors for the model are independent; however, they may not be satisfied in practice. In this study, we investigated the estimation for the varying coefficient model with correlated errors via B-spline. The B-spline approach, as a global smoothing method, is computationally efficient. Under suitable conditions, the convergence rates of the proposed estimators were obtained. Furthermore, two simulation examples were employed to demonstrate the performance of the proposed approach and the necessity of considering correlated errors.</p></abstract>

Additive varying-coefficient model for nonlinear gene-environment interactions

2018 ◽  
Vol 17 (2) ◽  
Author(s):  
Cen Wu ◽  
Ping-Shou Zhong ◽  
Yuehua Cui
Keyword(s):  
Variable Selection ◽  
Complex Disease ◽  
Convergence Rates ◽  
Regularity Conditions ◽  
Varying Coefficient Model ◽  
Two Stage ◽  
Absolute Deviation ◽  
Gene Set ◽  
Varying Coefficient ◽  
Gene Environment

Abstract Gene-environment (G×E) interaction plays a pivotal role in understanding the genetic basis of complex disease. When environmental factors are measured continuously, one can assess the genetic sensitivity over different environmental conditions on a disease trait. Motivated by the increasing awareness of gene set based association analysis over single variant based approaches, we proposed an additive varying-coefficient model to jointly model variants in a genetic system. The model allows us to examine how variants in a gene set are moderated by an environment factor to affect a disease phenotype. We approached the problem from a variable selection perspective. In particular, we select variants with varying, constant and zero coefficients, which correspond to cases of G×E interaction, no G×E interaction and no genetic effect, respectively. The procedure was implemented through a two-stage iterative estimation algorithm via the smoothly clipped absolute deviation penalty function. Under certain regularity conditions, we established the consistency property in variable selection as well as effect separation of the two stage iterative estimators, and showed the optimal convergence rates of the estimates for varying effects. In addition, we showed that the estimate of non-zero constant coefficients enjoy the oracle property. The utility of our procedure was demonstrated through simulation studies and real data analysis.

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