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利用传播方法调节逐点自适应估计参数AI 解读

This paper discusses the problem of adaptive estimation of a univariate object like the value of a regression function at a given point or a linear functional in a linear inverse problem. We consider an adaptive procedure originated from Lepski [Theory Probab. Appl. 35 (1990) 454–466.] that selects in a data-driven way one estimate out of a given class of estimates ordered by their variability. A serious problem with using this and similar procedures is the choice of some…

评估函数型数据的有限维性AI 解读

Summary If a problem in functional data analysis is low dimensional then the methodology for its solution can often be reduced to relatively conventional techniques in multivariate analysis. Hence, there is intrinsic interest in assessing the finite dimensionality of functional data. We show that this problem has several unique features. From some viewpoints the problem is trivial, in the sense that continuously distributed functional data which are exactly finite…

经验主成分函数极值的评估AI 解读

The difficulties of estimating and representing the distributions of functional data mean that principal component methods play a substantially greater role in functional data analysis than in more conventional finite-dimensional settings. Local maxima and minima in principal component functions are of direct importance; they indicate places in the domain of a random function where influence on the function value tends to be relatively strong but of opposite sign. We explore…