论文标题
当地弗雷切特回归的均匀收敛，并应用于定位超值和时间扭曲的度量空间轨迹轨迹
Uniform convergence of local Fréchet regression, with applications to locating extrema and time warping for metric space valued trajectories
论文作者
论文摘要
局部Fréchet回归是一种用于度量空间值响应和欧几里得预测变量的非参数回归方法，可以利用从噪音度量空间中的普通度量空间中获得值的平滑轨迹的估计值。我们得出了统一的收敛速率，到目前为止，对于固定目标和随机目标轨迹，我们对此方法进行了理论分析，在这些轨迹中，我们利用经验过程中使用工具。这些结果被证明广泛适用于度量空间价值数据分析。除了模拟外，我们还提供了两个相关示例，其中这些结果很重要：对公制空间中正确定义的极值位置的位置的一致估算值轨迹有价值的轨迹，我们用fMRI数据获得的定位最小大脑连接年龄的问题进行了说明；指标空间估值轨迹的时间扭曲，以不同国家的年龄分配为例。
Local Fréchet regression is a nonparametric regression method for metric space valued responses and Euclidean predictors, which can be utilized to obtain estimates of smooth trajectories taking values in general metric spaces from noisy metric space valued random objects. We derive uniform rates of convergence, which so far have eluded theoretical analysis of this method, for both fixed and random target trajectories, where we utilize tools from empirical processes. These results are shown to be widely applicable in metric space valued data analysis. In addition to simulations, we provide two pertinent examples where these results are important: The consistent estimation of the location of properly defined extrema in metric space valued trajectories, which we illustrate with the problem of locating the age of minimum brain connectivity as obtained from fMRI data; Time warping for metric space valued trajectories, illustrated with yearly age-at-death distributions for different countries.
