论文标题
对数 - 欧几里德歧管中SPD矩阵的内在小波估计值的统计推断
Statistical inference for intrinsic wavelet estimators of SPD matrices in a log-Euclidean manifold
论文作者
论文摘要
在本文中，我们将统计推断用于对数 - 欧几里得歧管中对称阳性定位（SPD）矩阵的固有小波估计量。该估计器可保留正定性并享有置换式等值，这与协方差矩阵特别相关。我们的第二代小波估计量基于平均插值，并且允许具有相同的强大属性，包括快速算法，从非参数曲线估计中已知，并在标准欧几里得设置中带有小波。 我们工作的核心是我们在非欧盟几何形状中高水平小波估计量的置信设置的主张。我们得出了该估计量的渐近正态性，包括其渐近方差的显式表达式。这为构建渐近置信区域打开了大门，我们将其与提议的推理方案进行比较。详细的数值模拟证实了我们建议的推理方案的适当性。
In this paper we treat statistical inference for an intrinsic wavelet estimator of curves of symmetric positive definite (SPD) matrices in a log-Euclidean manifold. This estimator preserves positive-definiteness and enjoys permutation-equivariance, which is particularly relevant for covariance matrices. Our second-generation wavelet estimator is based on average-interpolation and allows the same powerful properties, including fast algorithms, known from nonparametric curve estimation with wavelets in standard Euclidean set-ups. The core of our work is the proposition of confidence sets for our high-level wavelet estimator in a non-Euclidean geometry. We derive asymptotic normality of this estimator, including explicit expressions of its asymptotic variance. This opens the door for constructing asymptotic confidence regions which we compare with our proposed bootstrap scheme for inference. Detailed numerical simulations confirm the appropriateness of our suggested inference schemes.
