Related papers: An effective estimation of multivariate density fu…
A density estimation method in a Bayesian nonparametric framework is presented when recorded data are not coming directly from the distribution of interest, but from a length biased version. From a Bayesian perspective, efforts to…
In many practices, scientists are particularly interested in detecting which of the predictors are truly associated with a multivariate response. It is more accurate to model multiple responses as one vector rather than separating each…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
We derive asymptotic normality of kernel type deconvolution estimators of the density, the distribution function at a fixed point, and of the probability of an interval. We consider the so called super smooth case where the characteristic…
It is common, in deconvolution problems, to assume that the measurement errors are identically distributed. In many real-life applications, however, this condition is not satisfied and the deconvolution estimators developed for…
We consider the problem of estimating a spatially varying density function, motivated by problems that arise in large-scale radiological survey and anomaly detection. In this context, the density functions to be estimated are the background…
In this paper, we investigate the asymptotic properties of nonparametric Bayesian mixtures of Betas for estimating a smooth density on $[0,1]$. We consider a parametrization of Beta distributions in terms of mean and scale parameters and…
Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear…
Accurate approximation of the sampling distribution of nonparametric kernel density estimators is crucial for many statistical inference problems. Since these estimators have complex asymptotic distributions, bootstrap methods are often…
In the analysis of spatial point patterns on linear networks, a critical statistical objective is estimating the first-order intensity function, representing the expected number of points within specific subsets of the network. Typically,…
We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining…
Density estimation in high-dimensional settings is an important and challenging statistical problem.Traditional methods based on kernel smoothing are inefficient in high dimensions due to the difficulties in specifying appropriate…
We are interested in the rate of consistency of kernel density estimators with respect to the weighted sup-norm determined by some unbounded weight function. This problem has been considered by Gine, Koltchinskii and Zinn (2004) for a…
We address the problem of density estimation with $\mathbb{L}_s$-loss by selection of kernel estimators. We develop a selection procedure and derive corresponding $\mathbb{L}_s$-risk oracle inequalities. It is shown that the proposed…
Associated kernels have been introduced to improve the classical continuous kernels for smoothing any functional on several kinds of supports such as bounded continuous and discrete sets. This work deals with the effects of combined…
Kernel density estimation is a well known method involving a smoothing parameter (the bandwidth) that needs to be tuned by the user. Although this method has been widely used the bandwidth selection remains a challenging issue in terms of…
The present paper studies density deconvolution in the presence of small Berkson errors, in particular, when the variances of the errors tend to zero as the sample size grows. It is known that when the Berkson errors are present, in some…
It is shown that the Hall, Hu and Marron [Hall, P., Hu, T., and Marron J.S. (1995), Improved Variable Window Kernel Estimates of Probability Densities, {\it Annals of Statistics}, 23, 1--10] modification of Abramson's [Abramson, I. (1982),…
Estimators of information theoretic measures such as entropy and mutual information are a basic workhorse for many downstream applications in modern data science. State of the art approaches have been either geometric (nearest neighbor (NN)…
There is a rich literature on Bayesian methods for density estimation, which characterize the unknown density as a mixture of kernels. Such methods have advantages in terms of providing uncertainty quantification in estimation, while being…