标题： 一种用于估计移位曲线模型中共同形状的反褶积方法 显示英文标题

标题： A deconvolution approach to estimation of a common shape in a shifted curves model

摘要： 本文研究了随机位移曲线模型中自适应估计均值模式的问题。我们证明该问题可以转化为一个线性反问题，其中随机位移的密度扮演卷积算子的角色。提出了一种基于小波阈值的均值模式自适应估计器。我们研究了当观测曲线数量趋于无穷时，该估计器在二次风险下的收敛性，并表明该估计器在一大类Besov球上达到了接近最小最大收敛率。此收敛率不仅取决于曲线的共同形状的光滑性，还取决于随机位移密度的Fourier系数衰减速度。因此，本文将均值模式估计与线性反问题的统计分析联系起来，这是关于曲线配准和图像变形问题的一个新视角。我们还提供了一种估计曲线之间未知随机位移的新方法。一些数值实验被给出以展示我们方法的表现，并将其与其他文献中的算法进行比较。 显示英文摘要

摘要： This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role of a convolution operator. An adaptive estimator of the mean pattern, based on wavelet thresholding is proposed. We study its consistency for the quadratic risk as the number of observed curves tends to infinity, and this estimator is shown to achieve a near-minimax rate of convergence over a large class of Besov balls. This rate depends both on the smoothness of the common shape of the curves and on the decay of the Fourier coefficients of the density of the random shifts. Hence, this paper makes a connection between mean pattern estimation and the statistical analysis of linear inverse problems, which is a new point of view on curve registration and image warping problems. We also provide a new method to estimate the unknown random shifts between curves. Some numerical experiments are given to illustrate the performances of our approach and to compare them with another algorithm existing in the literature.