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边界估计AI 解读

A data set consists of independent observations taken at the nodes of a grid. An unknown boundary partitions the grid into two regions. All the observations coming from a particular region share a common distribution, but the distributions are different for the two different regions. These two distributions are entirely unknown and need not differ in their means, medians, or any other measure of “level.” The grid is of arbitrary dimension, and its mesh is rectangular. Our…

非参数变点估计AI 解读

Consider a sequence of independent random variables $\{X_i: 1 \leq i \leq n\}$ having cdf $F$ for $i \leq \theta n$ and cdf $G$ otherwise. A class of strongly consistent estimators for the change-point $\theta \in (0, 1)$ is proposed. The estimators require no knowledge of the functional forms or parametric families of $F$ and $G$. Furthermore, $F$ and $G$ need not differ in their means (or other measure of location). The only requirement is that $F$ and $G$ differ on a set…