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For data living in a manifold $M\subseteq \mathbb{R}^m$ and a point $p\in M$we consider a statistic $U_{k,n}$ which estimates the variance of the anglebetween pairs of vectors $X_i-p$ and $X_j-p$, for data points $X_i$, $X_j$,near $p$, and evaluate this statistic as a tool for estimation of the intrinsicdimension of $M$ at $p$. Consistency of the local dimension estimator isestablished and the asymptotic distribution of $U_{k,n}$ is found under minimalregularity assumptions. Performance of the proposed methodology is comparedagainst state-of-the-art methods on simulated data.

Local angles and dimension estimation from data on manifolds