Abstract
In this paper, we consider a general nonparametric regression estimation model with the feature of having multiplicative noise. We propose a linear estimator and nonlinear estimator by wavelet method. The convergence rates of those regression estimators under pointwise error over Besov spaces are proved. It turns out that the obtained convergence rates are consistent with the optimal convergence rate of pointwise nonparametric functional estimation.
Highlights
The regression estimation plays important roles in practical applications
This classical model is aimed at estimating the unknown regression function rðxÞ by the data ðU1, V1Þ, ðU2, V2Þ, ⋯, ðUn, VnÞ
The observed data contains some noise. In view of this case, this paper considers a regression estimation model with multiplicative noise
Summary
The regression estimation plays important roles in practical applications. The classical regression estimation model considers a strictly stationary random process fðUi, ViÞ, i ∈ Zg, which defined on 1⁄20, 1d × R and has a common density function g. Ð1Þ where ρðyÞ be a known function and hðxÞ stands for the density function of random variable U This classical model is aimed at estimating the unknown regression function rðxÞ by the data ðU1, V1Þ, ðU2, V2Þ, ⋯, ðUn, VnÞ. In view of this case, this paper considers a regression estimation model with multiplicative noise. The mean integrated square error of regression derivative estimators based on strong mixing data are discussed by Kou et al [6]. Those above results all only focus on global error. We assume that the regression function rðxÞ belongs to Besov ball with H > 0, i.e., n o
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