Nearest neighbor empirical processes. (arXiv:2110.15083v3 [math.ST] UPDATED)

In the regression framework, the empirical measure based on the responses
resulting from the nearest neighbors, among the covariates, to a given point
$x$ is introduced and studied as a central statistical quantity. First, the
associated empirical process is shown to satisfy a uniform central limit
theorem under a local bracketing entropy condition on the underlying class of
functions reflecting the localizing nature of the nearest neighbor algorithm.
Second a uniform non-asymptotic bound is established under a well-known
condition, often …

arxiv entropy framework math math.st neighbors process processes regression responses statistical theorem uniform