We study the problem nonparametric classification with repeated observations. Let $\bX$ be the $d$ dimensional feature vector and let $Y$ denote the label taking values in $\{1,\dots ,M\}$. In contrast to usual setup with large sample size $n$ and relatively low dimension $d$, this paper deals with the situation, when instead of observing a single feature vector $\bX$ we are given $t$ repeated feature vectors $\bV_1,\dots ,\bV_t $. Some simple classification rules are presented such that the conditional error probabilities have exponential convergence rate of convergence as $t\to\infty$. In the analysis, we investigate particular models like robust detection by nominal densities, prototype classification, linear transformation, linear classification, scaling.

翻译：我们研究带有重复观测的非参数分类问题。设 $\bX$ 为 $d$ 维特征向量，$Y$ 为取值于 $\{1,\dots ,M\}$ 的标签。与通常的大样本量 $n$ 和相对低维度 $d$ 的设置不同，本文处理的情形是：我们不是观测单个特征向量 $\bX$，而是获得 $t$ 个重复特征向量 $\bV_1,\dots ,\bV_t$。我们提出了一些简单的分类规则，使得当 $t\to\infty$ 时，条件错误概率具有指数收敛速率。在分析中，我们研究了特定模型，如基于名义密度的鲁棒检测、原型分类、线性变换、线性分类以及尺度缩放。