Related papers: Nonparametric Regression under Cluster Sampling
In this paper, we study classification and regression error bounds for inhomogenous data that are independent but not necessarily identically distributed. First, we consider classification of data in the presence of non-stationary noise and…
In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region which is defined by a set of linear inequalities involving…
Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic…
In this article, we propose a new nonparametric data analysis tool, which we call nonparametric modal regression, to investigate the relationship among interested variables based on estimating the mode of the conditional density of a…
This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…
We propose a general nonparametric Bayesian framework for binary regression, which is built from modeling for the joint response-covariate distribution. The observed binary responses are assumed to arise from underlying continuous random…
The global clustering coefficient is an effective measure for analyzing and comparing the structures of complex networks. The random annulus graph is a modified version of the well-known Erd\H{o}s-R\'{e}nyi random graph. It has been…
This paper provides new uniform rate results for kernel estimators of absolutely regular stationary processes that are uniform in the bandwidth and in infinite-dimensional classes of dependent variables and regressors. Our results are…
This paper considers a class of nonparametric autoregressive models with nonstationarity. We propose a nonparametric kernel test for the conditional mean and then establish an asymptotic distribution of the proposed test. Both the setting…
We provide uniform convergence rates for kernel averages on $[0,1]$ under equally-spaced fixed design points of the form $x_{t,T}=t/T,\ t\in\{1,\dotsc, T\},\ T\in\mathbb{N}$. The rates of weak and strong uniform consistency are derived…
We develop a clustering framework for observations from a population with a smooth probability distribution function and derive its asymptotic properties. A clustering criterion based on a linear combination of order statistics is proposed.…
Treatment noncompliance is pervasive in infectious disease cluster-randomized trials. Although all individuals within a cluster are assigned the same treatment condition, the treatment uptake status may vary across individuals due to…
The increasing availability of multiple network data has highlighted the need for statistical models for heterogeneous populations of networks. A convenient framework makes use of metrics to measure similarity between networks. In this…
We consider the problem of detecting whether or not, in a given sensor network, there is a cluster of sensors which exhibit an "unusual behavior." Formally, suppose we are given a set of nodes and attach a random variable to each node. We…
We study nonparametric regression and classification for path-valued data. We introduce a functional Nadaraya-Watson estimator that combines the signature transform from rough path theory with local kernel regression. The signature…
A new clustering accuracy measure is proposed to determine the unknown number of clusters and to assess the quality of clustering of a data set given in any dimensional space. Our validity index applies the classical nonparametric…
A massive dataset often consists of a growing number of (potentially) heterogeneous sub-populations. This paper is concerned about testing various forms of heterogeneity arising from massive data. In a general nonparametric framework, a set…
In the context of estimating local modes of a conditional density based on kernel density estimators, we show that existing bandwidth selection methods developed for kernel density estimation are unsuitable for mode estimation. We propose…
Machine learning models will often fail when deployed in an environment with a data distribution that is different than the training distribution. When multiple environments are available during training, many methods exist that learn…
We propose a flexible nonparametric regression method for ultrahigh-dimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. Then, an iterative…