On $L_2$-consistency of nearest neighbor matching

Causal nearest neighbor rules for optimal treatment regimes

The estimation of optimal treatment regimes is of considerable interest to precision medicine. In this work, we propose a causal $k$-nearest neighbor method to estimate the optimal treatment regime. The method roots in the framework of causal inference, and estimates the causal treatment effects within the nearest neighborhood. Although the method is simple, it possesses nice theoretical properties. We show that the causal $k$-nearest neighbor regime is universally consistent. That is, the causal $k$-nearest neighbor regime will eventually learn the optimal treatment regime as the sample size …

Rates of Convergence for Nearest Neighbor Classification

Nearest neighbor methods are a popular class of nonparametric estimators with several desirable properties, such as adaptivity to different distance scales in different regions of space. Prior work on convergence rates for nearest neighbor classification has not fully reflected these subtle properties. We analyze the behavior of these estimators in metric spaces and provide finite-sample, distribution-dependent rates of convergence under minimal assumptions. As a by-product, we are able to establish the universal consistency of nearest neighbor in a broader range of data spaces than was previo…

An Affine Invariant $k$-Nearest Neighbor Regression Estimate

We design a data-dependent metric in $\mathbb R^d$ and use it to define the $k$-nearest neighbors of a given point. Our metric is invariant under all affine transformations. We show that, with this metric, the standard $k$-nearest neighbor regression estimate is asymptotically consistent under the usual conditions on $k$, and minimal requirements on the input data.

依赖采样下的最近邻半径

Nearest-Neighbor Radii under Dependent Sampling

研究依赖采样下最近邻半径的几何性质，建立分布无关的几乎必然收敛和尖锐非渐近矩界，适用于高维数据集中的低维流形。

基于最近邻图的 Varentropy 估计

Varentropy Estimation via Nearest Neighbor Graphs

本文提出基于最近邻图的随机向量 Varentropy 统计估计量，并证明了其渐近无偏性与 L2 一致性。

k-Nearest neighbor density estimation on Riemannian Manifolds

In this paper, we consider a k-nearest neighbor kernel type estimator when the random variables belong in a Riemannian manifolds. We study asymptotic properties such as the consistency and the asymptotic distribution. A simulation study is also consider to evaluate the performance of the proposal. Finally, to illustrate the potential applications of the proposed estimator, we analyzed two real example where two different manifolds are considered.