Related papers: Reducing bias in nonparametric density estimation …
The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…
A kernel density estimator for data on the polysphere $\mathbb{S}^{d_1}\times\cdots\times\mathbb{S}^{d_r}$, with $r,d_1,\ldots,d_r\geq 1$, is presented in this paper. We derive the main asymptotic properties of the estimator, including mean…
We develop and analyze a principled approach to kernel ridge regression under covariate shift. The goal is to learn a regression function with small mean squared error over a target distribution, based on unlabeled data from there and…
Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…
We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative.…
Recent work has focused on the problem of nonparametric estimation of information divergence functionals. Many existing approaches are restrictive in their assumptions on the density support set or require difficult calculations at the…
We present a local density estimator based on first order statistics. To estimate the density at a point, $x$, the original sample is divided into subsets and the average minimum sample distance to $x$ over all such subsets is used to…
For the kernel estimator of the quantile density function (the derivative of the quantile function), I show how to perform the boundary bias correction, establish the rate of strong uniform consistency of the bias-corrected estimator, and…
New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…
An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness…
In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…
Nonparametric estimation of copula density functions using kernel estimators presents significant challenges. One issue is the potential unboundedness of certain copula density functions at the corners of the unit square. Another is the…
This paper studies nonparametric regression with long memory (LRD) errors and predictors. First, we formulate general conditions which guarantee the standard rate of convergence for a nonparametric kernel estimator. Second, we calculate the…
Copula modelling has become ubiquitous in modern statistics. Here, the problem of nonparametrically estimating a copula density is addressed. Arguably the most popular nonparametric density estimator, the kernel estimator is not suitable…
This paper describes how to specify probability models for data analysis via a backward induction procedure. The new approach yields coherent, prior-free uncertainty assessment. After presenting some intuition-building examples, the new…
Local polynomial regression of order at least one often performs poorly in regions of sparse data. Local constant regression is exceptional in this regard, though it is the least accurate method in general, especially at the boundaries of…
We propose a novel method for density estimation that leverages an estimated score function to debias kernel density estimation (SD-KDE). In our approach, each data point is adjusted by taking a single step along the score function with a…
This study proposes a mathematical programming-based algorithm for the integrated selection of variable subsets and bandwidth estimation in geographically weighted regression, a local regression method that allows the kernel bandwidth and…
In the mean-median-mode triad of univariate centrality measures, the mode has been overlooked for estimating the center of symmetry in continuous and unimodal settings. This paper expands on the connection between kernel mode estimators and…
We introduce a general method to prove uniform in bandwidth consistency of kernel-type function estimators. Examples include the kernel density estimator, the Nadaraya-Watson regression estimator and the conditional empirical process. Our…