Empirical geometry of multivariate data: a deconvolution approach
多元数据的经验几何：反卷积方法
Let $\{Y_j : j = 1,\ldots,n\}$ be independent observations in $\mathbb{R}^m, m \geq 1$ with common distribution $Q$. Suppose that $Y_j = X_j + \xi_j, j = 1,\ldots,n$, where $\{X_j, \xi_j, j = 1,\ldots,n\}$ are independent, $X_ j, j = 1,\ldots,n$ have common distribution $P$ and $\xi_ j, j = 1, \ldots,n$ have common distribution $\mu$, so that $Q = P * \mu$. The problem is to recover hidden geometric structure of the support of $P$ based on the independent observations $Y_j$.…