B-spline estimation in varying coefficient models with correlated errors

Yanping Liu; Juliang Yin; Yanping Liu; Juliang Yin

doi:10.3934/math.2022195

AIMS Mathematics

2022, Volume 7, Issue 3: 3509-3523. doi: 10.3934/math.2022195

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Research article

B-spline estimation in varying coefficient models with correlated errors

Yanping Liu ,
Juliang Yin ^,

School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China

Received: 13 August 2021 Accepted: 23 November 2021 Published: 02 December 2021
MSC : 62G08, 62M10, 65D07

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.
- varying coefficient models,
- nonlinear time series,
- B-spline estimation,
- consistency,
- generalized least squares method
Citation: Yanping Liu, Juliang Yin. B-spline estimation in varying coefficient models with correlated errors[J]. AIMS Mathematics, 2022, 7(3): 3509-3523. doi: 10.3934/math.2022195

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Abstract

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.

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