Related papers: Nearest neighbor empirical processes

Clustered sampling is prevalent in empirical regression discontinuity (RD) designs, but it has not received much attention in the theoretical literature. In this paper, we introduce a general model-based framework for such settings and…

We introduce a novel \textit{k}-nearest neighbor (\textit{k}-NN) regression method for joint estimation of the conditional mean and variance. The proposed algorithm preserves the computational efficiency and manifold-learning capabilities…

This paper presents a general framework for the estimation of regression models with circular covariates, where the conditional distribution of the response given the covariate can be specified through a parametric model. The estimation of…

We study the empirical measure of the output of the t-distributed stochastic neighbour embedding algorithm when the initial data is given by n independent, identically distributed inputs. We prove that under certain assumptions on the…

We consider nearest neighbor spacing distributions of composite ensembles of levels. These are obtained by combining independently unfolded sequences of levels containing only few levels each. Two problems arise in the spectral analysis of…

In this paper we present a series of results that permit to extend in a direct manner uniform deviation inequalities of the empirical process from the independent to the dependent case characterizing the additional error in terms of…

Consider a stationary Poisson process $\eta$ in the $d$-dimensional Euclidean or hyperbolic space and construct a random graph with vertex set $\eta$ as follows. First, each point $x\in\eta$ is connected by an edge to its nearest neighbour,…

When the competing classes in a classification problem are not of comparable size, many popular classifiers exhibit a bias towards larger classes, and the nearest neighbor classifier is no exception. To take care of this problem, we develop…

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory.…

Consider a network whose nodes have some initial values, and it is desired to design an algorithm that builds on neighbor to neighbor interactions with the ultimate goal of convergence to the average of all initial node values or to some…

In this paper we apply Conformal Prediction (CP) to the k-Nearest Neighbours Regression (k-NNR) algorithm and propose ways of extending the typical nonconformity measure used for regression so far. Unlike traditional regression methods…

We establish the first nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators where feature vectors reside in metric spaces. Our bounds imply rates of strong consistency for these…

This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…

A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…

We address the inference problem concerning regression coefficients in a classical linear regression model using least squares estimates. The analysis is conducted under circumstances where network dependency exists across units in the…

Consider a measure $\mu_\lambda = \sum_x \xi_x \delta_x$ where the sum is over points $x$ of a Poisson point process of intensity $\lambda$ on a bounded region in $d$-space, and $\xi_x$ is a functional determined by the Poisson points near…

This paper develops a class of Bayesian non- and semiparametric methods for estimating regression curves and surfaces. The main idea is to model the regression as locally linear, and then place suitable local priors on the local parameters.…

In this paper, we apply conformal prediction to time series data. Conformal prediction isa method that produces predictive regions given a confidence level. The regions outputs arealways valid under the exchangeability assumption. However,…

Gaussian process ($GP$) regression is a widely used non-parametric modeling tool, but its cubic complexity in the training size limits its use on massive data sets. A practical remedy is to predict using only the nearest neighbours of each…

This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to…