Related papers: Multivariate Density Estimation via Adaptive Parti…
We consider density estimators based on the nearest neighbors method applied to discrete point distibutions in spaces of arbitrary dimensionality. If the density is constant, the volume of a hypersphere centered at a random location is…
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 propose the density ratio permutation test, a hypothesis test that assesses whether the ratio between two densities is proportional to a known function based on independent samples from each distribution. The test uses an efficient…
We construct an adaptive estimator of a density function on $d$ dimensional unit sphere $S^d$ ($d \geq 2 $), using a new type of spherical frames. The frames, or as we call them, stereografic wavelets are obtained by transforming a wavelet…
The assumption of log-concavity is a flexible and appealing nonparametric shape constraint in distribution modelling. In this work, we study the log-concave maximum likelihood estimator (MLE) of a probability mass function (pmf). We show…
While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel…
We investigate density estimation from a $n$-sample in the Euclidean space $\mathbb R^D$, when the data is supported by an unknown submanifold $M$ of possibly unknown dimension $d < D$ under a reach condition. We study nonparametric kernel…
Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias…
The density ratio model (DRM) provides a flexible and useful platform for combining information from multiple sources. In this paper, we consider statistical inference under two-sample DRMs with additional parameters defined through and/or…
We study the nonparametric maximum likelihood estimator (NPMLE) for Gaussian and Poisson mixture models, assuming the support of the true mixing distribution lies in a fixed bounded set. In this setting, we establish exact parametric rates…
Mixture models are regularly used in density estimation applications, but the problem of estimating the mixing distribution remains a challenge. Nonparametric maximum likelihood produce estimates of the mixing distribution that are…
Let $\textbf{X} = (X_1,\ldots, X_p)$ be a stochastic vector having joint density function $f_{\textbf{X}}(x)$ with partitions $\textbf{X}_1 = (X_1,\ldots, X_k)$ and $\textbf{X}_2 = (X_{k+1},\ldots, X_p)$. A new method for estimating the…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
We consider a semiparametric mixture of two univariate density functions where one of them is known while the weight and the other function are unknown. Such mixtures have a history of application to the problem of detecting differentially…
We consider a nonparametric regression model $Y=r(X)+\varepsilon$ with a random covariate $X$ that is independent of the error $\varepsilon$. Then the density of the response $Y$ is a convolution of the densities of $\varepsilon$ and…
We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By…
A nonparametric and locally adaptive Bayesian estimator is proposed for estimating a binary regression. Flexibility is obtained by modeling the binary regression as a mixture of probit regressions with the argument of each probit regression…
In this article, we revisit the problem of estimating the unknown zero-symmetric distribution in a two-component location mixture model, considered in previous works, now under the assumption that the zero-symmetric distribution has a…
We study the problem of the non-parametric estimation for the density $\pi$ of the stationary distribution of a stochastic two-dimensional damping Hamiltonian system $(Z_t)_{t\in[0,T]}=(X_t,Y_t)_{t \in [0,T]}$. From the continuous…
We consider the problem of Bayesian density estimation on the positive semiline for possibly unbounded densities. We propose a hierarchical Bayesian estimator based on the gamma mixture prior which can be viewed as a location mixture. We…