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We consider the problem of minimizing a given $n$-variate polynomial $f$ over the hypercube $[-1,1]^n$. An idea introduced by Lasserre, is to find a probability distribution on $[-1,1]^n$ with polynomial density function $h$ (of given…

Optimization and Control · Mathematics 2017-07-03 Etienne de Klerk , Roxana Hess , Monique Laurent

Motivated by applications in statistics and machine learning, we consider a problem of unmixing convex combinations of nonparametric densities. Suppose we observe $n$ groups of samples, where the $i$th group consists of $N_i$ independent…

Statistics Theory · Mathematics 2026-03-31 Jianqing Fan , Zheng Tracy Ke , Zhaoyang Shi

We study the rates of estimation of finite mixing distributions, that is, the parameters of the mixture. We prove that under some regularity and strong identifiability conditions, around a given mixing distribution with $m_0$ components,…

Statistics Theory · Mathematics 2015-07-16 Philippe Heinrich , Jonas Kahn

A new maximum likelihood method for deconvoluting a continuous density with a positive lower bound on a known compact support in additive measurement error models with known error distribution using the approximate Bernstein type polynomial…

Methodology · Statistics 2018-01-30 Zhong Guan

We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…

Statistics Theory · Mathematics 2016-02-02 Nicolas Asin , Jan Johannes

We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape…

Methodology · Statistics 2015-11-10 Rohit Kumar Patra , Bodhisattva Sen

This paper deals with nonparametric estimation of conditional den-sities in mixture models in the case when additional covariates are available. The proposed approach consists of performing a prelim-inary clustering algorithm on the…

Statistics Theory · Mathematics 2015-02-09 Stéphane Auray , Nicolas Klutchnikoff , Laurent Rouvière

Motivated by fluorescence lifetime measurements this paper considers the problem of nonparametric density estimation in the pile-up model. Adaptive nonparametric estimators are proposed for the pile-up model in its simple form as well as in…

Applications · Statistics 2010-11-03 Fabienne Comte , Tabea Rebafka

In this paper, we introduce a new estimator for the emission densities of a nonparametric hidden Markov model. It is adaptive and minimax with respect to each state's regularity--as opposed to globally minimax estimators, which adapt to the…

Statistics Theory · Mathematics 2018-07-17 Luc Lehéricy

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…

Statistics Theory · Mathematics 2017-08-01 Zhou Shen , Michael Levine , Zuofeng Shang

In this paper we consider non parametric finite translation mixtures. We prove that all the parameters of the model are identifiable as soon as the matrix that defines the joint distribution of two consecutive latent variables is non…

Statistics Theory · Mathematics 2013-02-12 Elisabeth Gassiat , Judith Rousseau

We investigate Bayesian nonparametric density estimation via orthogonal polynomial expansions in weighted Sobolev spaces. A core challenge is establishing minimax optimal posterior convergence rates, especially for densities on unbounded…

Statistics Theory · Mathematics 2026-03-20 Yiqi Luo , Xue Luo

Non-linear aggregation strategies have recently been proposed in response to the problem of how to combine, in a non-linear way, estimators of the regression function (see for instance \cite{biau:16}), classification rules (see…

Statistics Theory · Mathematics 2018-12-24 Alejandro Cholaquidis , Ricardo Fraiman , Badih Ghattas , Juan Kalemkerian

We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions.…

Methodology · Statistics 2025-02-28 M. E. J. Newman

We study a nonparametric regression model for sample data which is defined on an $N$-dimensional lattice structure and which is assumed to be strong spatial mixing: we use design adapted multidimensional Haar wavelets which form an…

Statistics Theory · Mathematics 2017-07-31 Johannes T. N. Krebs

We propose a novel approach for density estimation called histogram trend filtering. Our estimator arises from looking at surrogate Poisson model for counts of observations in a partition of the support of the data. We begin by showing…

Methodology · Statistics 2016-02-09 Oscar Hernan Madrid Padilla , James G. Scott

This paper outlines a new nonparametric estimation procedure for unobserved phi-mixing processes. It is assumed that the only information on the stationary hidden states (Xk) is given by the process (Yk), where Yk is a noisy observation of…

Statistics Theory · Mathematics 2015-08-27 Thierry Dumont , Sylvain Le Corff

Although continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to…

Statistics Theory · Mathematics 2014-05-26 Antonio Canale , David B. Dunson

As we collect additional samples from a data population for which a known density function estimate may have been previously obtained by a black box method, the increased complexity of the data set may result in the true density being…

Machine Learning · Statistics 2022-10-28 Dat Do , Nhat Ho , XuanLong Nguyen

We propose a generative model that achieves minimax-optimal convergence rates for estimating probability distributions supported on unknown low-dimensional manifolds. Building on Fefferman's solution to the geometric Whitney problem, our…

Statistics Theory · Mathematics 2025-06-25 Arthur Stéphanovitch