Open AccessB-spline estimation in varying coefficient models with correlated errors
Author(s) -
Yan-Ping Liu,
AUTHOR_ID,
Juliang Yin
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022195
Subject(s) - estimator , smoothing spline , smoothing , curse of dimensionality , spline (mechanical) , mathematics , b spline , regression , convergence (economics) , computer science , statistics , algorithm , spline interpolation , engineering , mathematical analysis , structural engineering , economic growth , economics , bilinear interpolation
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.