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时间序列的粗笔变换AI 解读

Summary Traditional visualization of time series data often consists of plotting the time series values against time and ‘connecting the dots’. We propose an alternative, multiscale visualization technique, motivated by the scale–space approach in computer vision. In brief, our method also ‘connects the dots’ but uses a range of pens of varying thicknesses for this. The resulting multiscale map, which is termed the thick pen transform, corresponds to viewing the time series…

伪数据在稳健平滑中的作用及其小波回归应用AI 解读

We propose a robust curve and surface estimator based on M-type estimators and penalty-based smoothing. This approach also includes an application to wavelet regression. The concept of pseudo data, a transformation of the robust additive model to the one with bounded errors, is used to derive some theoretical properties and also motivate a computational algorithm. The resulting algorithm, termed the es-algorithm, is computationally fast and provides a simple way of choosing…

小波回归中的多项式边界处理AI 解读

To overcome boundary problems with wavelet regression, we propose a simple method that reduces bias at the boundaries. It is based on a combination of wavelet functions and low‐order polynomials. The utility of the method is illustrated with simulation studies and a real example. Asymptotic results show that the estimators are competitive with other nonparametric procedures.