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自适应小波估计：块阈值与oracle不等式方法AI 解读

We study wavelet function estimation via the approach of block thresholding and ideal adaptation with oracle. Oracle inequalities are derived and serve as guides for the selection of smoothing parameters. Based on an oracle inequality and motivated by the data compression and localization properties of wavelets, an adaptive wavelet estimator for nonparametric regression is proposed and the optimality of the procedure is investigated. We show that the estimator achieves…

非等间距样本的小波收缩AI 解读

Standard wavelet shrinkage procedures for nonparametric regression are restricted to equispaced samples. There, data are transformed into empirical wavelet coefficients and threshold rules are applied to the coefficients. The estimators are obtained via the inverse transform of the denoised wavelet coefficients. In many applications, however, the samples are nonequispaced. It can be shown that these procedures would produce suboptimal estimators if they were applied directly…