Wavelet estimations of the derivatives of variance function in heteroscedastic model

Junke Kou; Hao Zhang; Junke Kou; Hao Zhang

doi:10.3934/math.2023734

AIMS Mathematics

2023, Volume 8, Issue 6: 14340-14361. doi: 10.3934/math.2023734

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Research article

Wavelet estimations of the derivatives of variance function in heteroscedastic model

Junke Kou ^,,
Hao Zhang

School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China

Received: 22 February 2023 Revised: 01 April 2023 Accepted: 06 April 2023 Published: 18 April 2023
MSC : 62G07, 62G20, 42C40

This paper studies nonparametric estimations of the derivatives $ r^{(m)}(x) $ of the variance function in a heteroscedastic model. Using a wavelet method, a linear estimator and an adaptive nonlinear estimator are constructed. The convergence rates under $ L^{\tilde{p}} (1\leq \tilde{p} < \infty) $ risk of those two wavelet estimators are considered with some mild assumptions. A simulation study is presented to validate the performances of the wavelet estimators.
- nonparametric wavelet estimation,
- derivative function,
- heteroscedastic model,
- $ L^{\tilde{p}} $ risk
Citation: Junke Kou, Hao Zhang. Wavelet estimations of the derivatives of variance function in heteroscedastic model[J]. AIMS Mathematics, 2023, 8(6): 14340-14361. doi: 10.3934/math.2023734

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Abstract

This paper studies nonparametric estimations of the derivatives $ r^{(m)}(x) $ of the variance function in a heteroscedastic model. Using a wavelet method, a linear estimator and an adaptive nonlinear estimator are constructed. The convergence rates under $ L^{\tilde{p}} (1\leq \tilde{p} < \infty) $ risk of those two wavelet estimators are considered with some mild assumptions. A simulation study is presented to validate the performances of the wavelet estimators.

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