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Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…

Kernel estimation of a probability density function supported on the unit interval has proved difficult, because of the well known boundary bias issues a conventional kernel density estimator would necessarily face in this situation.…

One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…

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…

One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the…

Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel…

In this work we give new density estimators by averaging classical density estimators such as the histogram, the frequency polygon and the kernel density estimators obtained over different bootstrap samples of the original data. We prove…

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…

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…

Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher…

This paper proposes a new method for estimating high-dimensional binary choice models. We consider a semiparametric model that places no distributional assumptions on the error term, allows for heteroskedastic errors, and permits endogenous…

Let $f$ be a multivariate density and $f\_n$ be a kernel estimate of $f$ drawn from the $n$-sample $X\_1,...,X\_n$ of i.i.d. random variables with density $f$. We compute the asymptotic rate of convergence towards 0 of the volume of the…

In this paper, we study the Bernstein polynomial model for estimating the multivariate distribution functions and densities with bounded support. As a mixture model of multivariate beta distributions, the maximum (approximate) likelihood…

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…

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…

In this paper we introduce a method for nonparametric density estimation on geometric networks. We define fused density estimators as solutions to a total variation regularized maximum-likelihood density estimation problem. We provide…

Nonparametric density estimators are studied for $d$-dimensional, strongly spatial mixing data which is defined on a general $N$-dimensional lattice structure. We consider linear and nonlinear hard thresholded wavelet estimators which are…

Multimodal regression estimation methods are introduced for regression models involving circular response and/or covariate. The regression estimators are based on the maximization of the conditional densities of the response variable over…

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…

We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage…