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基于最近邻的多元两样本检验AI 解读

A new class of simple tests is proposed for the general multivariate two-sample problem based on the (possibly weighted) proportion of all k nearest neighbor comparisons in which observations and their neighbors belong to the same sample. Large values of the test statistics give evidence against the hypothesis H of equality of the two underlying distributions. Asymptotic null distributions are explicitly determined and shown to involve certain nearest neighbor interaction…

最近邻拟合优度检验的无限维近似AI 解读

Let $X_1, \cdots, X_n$ be i.i.d. $\mathbb{R}^m$-valued observations from a bounded density $g(x)$ continuous on its support. Let $W_i = \exp\{- ng(X_i)V(R_i)\}, i = 1, \cdots, n$, where $V(R_i)$ is the volume of the nearest neighbor sphere around $X_i$, and let $w(x)$ be any bounded continuous weight function on $\mathbb{R}^m$. An infinite-dimensional approximation to the asymptotic form of the weighted empirical distribution function of the $W_i$'s is presented. The…

基于最近邻统计量加权经验分布的多维拟合优度检验AI 解读

Let $X_1, \cdots, X_n$ be a random sample in $\mathbb{R}^m$ from an unknown density $f(x)$. Recently Bickel and Breiman have introduced a goodness of fit test for this situation based on the empirical distribution function of the variables $W_i = \exp\{-ng(X_i)V(R_i)\}, i = 1, \cdots, n$, where $g(x)$ is the hypothesized density and $V(R_i)$ represents the volume of the nearest neighbor sphere centered at $X_i$. Under the null hypothesis $H : f(x) = g(x)$, the empirical…