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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…

Methodology · Statistics 2018-07-13 Denis Belomestny , Alexander Goldenshluger

In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit…

Statistics Theory · Mathematics 2026-02-12 Hyeok Kyu Kwon , Dongha Kim , Ilsang Ohn , Minwoo Chae

We introduce PMODE (Partitioned Mixture Of Density Estimators), a general and modular framework for mixture modeling with both parametric and nonparametric components. PMODE builds mixtures by partitioning the data and fitting separate…

Machine Learning · Computer Science 2025-09-01 Robert A. Vandermeulen

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…

Statistics Theory · Mathematics 2020-02-25 Natalia Bochkina , Judith Rousseau

Mixture models are widely used in modeling heterogeneous data populations. A standard approach of mixture modeling assumes that the mixture component takes a parametric kernel form. In many applications, making parametric assumptions on the…

Methodology · Statistics 2026-03-06 Yilei Zhang , Yun Wei , Aritra Guha , XuanLong Nguyen

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…

Statistics Theory · Mathematics 2020-11-02 Clément Berenfeld , Marc Hoffmann

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…

Methodology · Statistics 2019-01-23 Tao Wang , Zhong Guan

We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…

Machine Learning · Statistics 2026-05-26 Mohammadreza Ahmadypour , Tara Javidi , Farinaz Koushanfar

Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…

Statistics Theory · Mathematics 2011-09-26 Debdeep Pati , Anirban Bhattacharya , David B. Dunson

This paper develops a nonparametric density estimator with parametric overtones. Suppose $f(x,\theta)$ is some family of densities, indexed by a vector of parameters $\theta$. We define a local kernel smoothed likelihood function which for…

Methodology · Statistics 2026-04-22 Nils Lid Hjort , M. C. Jones

The Dirichlet process mixture model and more general mixtures based on discrete random probability measures have been shown to be flexible and accurate models for density estimation and clustering. The goal of this paper is to illustrate…

Methodology · Statistics 2013-10-02 Ernesto Barrios , Antonio Lijoi , Luis E. Nieto-Barajas , Igor Prünster

Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…

Statistics Theory · Mathematics 2017-01-27 Shuang Zhou , Debdeep Pati , Anirban Bhattacharya , David Dunson

Finite mixture models are widely used in econometric analyses to capture unobserved heterogeneity. This paper shows that maximum likelihood estimation of finite mixtures of parametric densities can suffer from substantial finite-sample bias…

Methodology · Statistics 2026-02-04 Raphaël Langevin

In this paper, we develop a finite mixture of convolutional distributions, a statistical model to analyze continuous data distributed approximately on a mixture of low-dimensional affine subspaces. The observations are assumed independent…

Statistics Theory · Mathematics 2026-04-21 Sunrit Chakraborty , XuanLong Nguyen

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…

Statistics Theory · Mathematics 2010-01-12 Judith Rousseau

We consider the problem of estimating a density $f_X$ using a sample $Y_1,...,Y_n$ from $f_Y=f_X\star f_{\epsilon}$, where $f_{\epsilon}$ is an unknown density. We assume that an additional sample $\epsilon_1,...,\epsilon_m$ from…

Statistics Theory · Mathematics 2009-08-21 Jan Johannes

Estimating the mixing density of a latent mixture model is an important task in signal processing. Nonparametric maximum likelihood estimation is one popular approach to this problem. If the latent variable distribution is assumed to be…

Methodology · Statistics 2024-03-01 Shijie Wang , Minsuk Shin , Ray Bai

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…

Other Statistics · Statistics 2018-03-05 Hien D. Nguyen , Geoffrey J. McLachlan

A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly…

Statistics Theory · Mathematics 2021-02-08 Gaelle Chagny , Antoine Channarond , Van Ha Hoang , Angelina Roche

This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…

Methodology · Statistics 2019-05-07 Shyamalendu Sinha , Jeffrey D. Hart