论文标题
密度脊的渐近置信区
Asymptotic Confidence Regions for Density Ridges
论文作者
论文摘要
我们开发了大型样本理论，包括$ r $二维的概率密度功能的非参数置信区域，上面是$ \ mathbb {r}^d $，其中$ 1 \ leq r <d $。我们将脊视为某些特殊功能的水平集的交集。这些功能的插入式内核估计器的垂直变化被限制在山脊上，用作脊估计的最大偏差的量度。我们对山脊的置信区域是由这种最大偏差的渐近分布确定的，该分布是通过使用流形索引的非平稳$χ$场的极值分布来确定的。
We develop large sample theory including nonparametric confidence regions for $r$-dimensional ridges of probability density functions on $\mathbb{R}^d$, where $1\leq r<d$. We view ridges as the intersections of level sets of some special functions. The vertical variation of the plug-in kernel estimators for these functions constrained on the ridges is used as the measure of maximal deviation for ridge estimation. Our confidence regions for the ridges are determined by the asymptotic distribution of this maximal deviation, which is established by utilizing the extreme value distribution of nonstationary $χ$-fields indexed by manifolds.
