Repeated Observations for Classification

We study the problem nonparametric classification with repeated observations. Let $\text{bX}$ 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 $\text{bX}$ we are given $t$ repeated feature vectors ${\text{bV}}_1,\dots ,{\text{bV}}_t$. Some simple classification rules are presented such that the conditional error probabilities have exponential convergence rate of convergence as $t\to \mathrm{\infty }$. In the analysis, we investigate particular models like robust detection by nominal densities, prototype classification, linear transformation, linear classification, scaling.