Affiliation:
1. School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China
Abstract
For derivative function estimation, conventional research only focuses on the derivative estimation of one-dimensional functions. This paper considers partial derivatives estimation of a multivariate variance function in a heteroscedastic model. A wavelet estimator of partial derivatives of a multivariate variance function is proposed. The convergence rates of a wavelet estimator under different estimation errors are discussed. It turns out that the strong convergence rate of the wavelet estimator is the same as the optimal uniform almost sure convergence rate of nonparametric function problems.
Funder
Guangxi Natural Science Foundation
National Natural Science Foundation of China
Center for Applied Mathematics of Guangxi
Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation
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