最近邻估计量收敛速率研究：在平滑回归函数情况下的表现

仿射不变的$k$ -最近邻回归估计

An Affine Invariant $k$-Nearest Neighbor Regression Estimate

我们在$\mathbb R^d$中设计了一个依赖于数据的度量，并使用它来定义给定点的$k$ -最近邻。我们的度量在所有的仿射变换下都是不变的。我们表明，与此度量，标准的$k$ -最近邻回归估计是渐近一致的$k$的通常条件下，对输入数据的最低要求。

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。

黎曼流形上的k-近邻密度估计

k-Nearest neighbor density estimation on Riemannian Manifolds

本文考虑了随机变量属于黎曼流形时的k-近邻核型估计。我们研究的渐近性质，如一致性和渐近分布。仿真研究也被认为是评估的建议的性能。最后，为了说明所提出的估计的潜在应用，我们分析了两个实际的例子，其中考虑两个不同的流形。

密度和回归函数的 $k$-最近邻核估计量的强一致一致性的收敛速率

Rates of strong uniform consistency for the $k$-nearest neighbors kernel estimators of density and regression function

本文探讨了多元情形下密度与回归函数的 $k$-最近邻核估计量的一致性问题，并在特定假设下推导出这些估计量在整个空间 $\mathbb{R}^p$ 上的强一致一致性的收敛速率。

Distributed Nearest Neighbor Classification

Nearest neighbor is a popular nonparametric method for classification and regression with many appealing properties. In the big data era, the sheer volume and spatial/temporal disparity of big data may prohibit centrally processing and storing the data. This has imposed considerable hurdle for nearest neighbor predictions since the entire training data must be memorized. One effective way to overcome this issue is the distributed learning framework. Through majority voting, the distributed nearest neighbor classifier achieves the same rate of convergence as its oracle version in terms of both …

k-nearest neighbors prediction and classification for spatial data

This paper proposes a spatial k-nearest neighbor method for nonparametric prediction of real-valued spatial data and supervised classification for categorical spatial data. The proposed method is based on a double nearest neighbor rule which combines two kernels to control the distances between observations and locations. It uses a random bandwidth in order to more appropriately fit the distributions of the covariates. The almost complete convergence with rate of the proposed predictor is established and the almost sure convergence of the supervised classification rule was deduced. Finite samp…