Related papers: Estimating Probability Distributions using "Dirac"…
We consider nonparametric estimation of the derivative of a probability density function with the bounded support on $[0,\infty)$. Estimates are looked up in the class of estimates with asymmetric gamma kernel functions. The use of gamma…
We provide a new method to approximate a (possibly discontinuous) function using Christoffel-Darboux kernels. Our knowledge about the unknown multivariate function is in terms of finitely many moments of the Young measure supported on the…
Proximity Distribution Kernel is an effective method for bag-of-featues based image representation. In this paper, we investigate the soft assignment of visual words to image features for proximity distribution. Visual word contribution…
In this paper we propose a new method of joint nonparametric estimation of probability density and its support. As is well known, nonparametric kernel density estimator has "boundary bias problem" when the support of the population density…
A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…
Important information concerning a multivariate data set, such as clusters and modal regions, is contained in the derivatives of the probability density function. Despite this importance, nonparametric estimation of higher order derivatives…
Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
Deep Neural Networks (DNNs) have performed admirably in classification tasks. However, the characterization of their classification uncertainties, required for certain applications, has been lacking. In this work, we investigate the issue…
We propose a new estimator for nonparametric binary choice models that does not impose a parametric structure on either the systematic function of covariates or the distribution of the error term. A key advantage of our approach is its…
We introduce a new class of nonparametric prior distributions on the space of continuously varying densities, induced by Dirichlet process mixtures which diffuse in time. These select time-indexed random functions without jumps, whose…
The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of…
We consider nonparametric prediction with multiple covariates, in particular categorical or functional predictors, or a mixture of both. The method proposed bases on an extension of the Nadaraya-Watson estimator where a kernel function is…
Within the study of uncertain dynamical systems, iterated random functions are a key tool. There, one samples a family of functions according to a stationary distribution. Here, we introduce an extension, where one sample functions…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
We consider the problem of constructing confidence intervals for nonparametric functional data analysis using empirical likelihood. In this doubly infinite-dimensional context, we demonstrate the Wilks's phenomenon and propose a…
Estimating the uncertainty in deep neural network predictions is crucial for many real-world applications. A common approach to model uncertainty is to choose a parametric distribution and fit the data to it using maximum likelihood…
We consider an empirical likelihood inference for parameters defined by general estimating equations when some components of the random observations are subject to missingness. As the nature of the estimating equations is wide-ranging, we…
Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…
Nonparametric kernel density and local polynomial regression estimators are very popular in Statistics, Economics, and many other disciplines. They are routinely employed in applied work, either as part of the main empirical analysis or as…