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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…
This work considers a problem of estimating a mixing probability density $f$ in the setting of discrete mixture models. The paper consists of three parts. The first part focuses on the construction of an $L_1$ consistent estimator of $f$.…
We compare two statistical models of three binary random variables. One is a mixture model and the other is a product of mixtures model called a restricted Boltzmann machine. Although the two models we study look different from their…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
In this article, we introduce finite mixture models (FMMs) renowned for capturing population heterogeneity. Our focus lies in establishing stochastic comparisons between two arithmetic (finite) mixture models, employing the vector…
In this paper, we discuss the application of extreme value theory in the context of stationary $\beta$-mixing sequences that belong to the Fr\'echet domain of attraction. In particular, we propose a methodology to construct bias-corrected…
Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…
This work introduces a new method for selecting the number of components in finite mixture models (FMMs) using variational Bayes, inspired by the large-sample properties of the Evidence Lower Bound (ELBO) derived from mean-field (MF)…
Motivated by two case studies using primary care records from the Clinical Practice Research Datalink, we describe statistical methods that facilitate the analysis of tall data, with very large numbers of observations. Our focus is on…
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…
This paper shows that large nonparametric classes of conditional multivariate densities can be approximated in the Kullback--Leibler distance by different specifications of finite mixtures of normal regressions in which normal means and…
Let $\eta=(\eta(t))_{t\in T}$ be a sample continuous max-infinitely random field on a locally compact metric space $T$. For a closed subset $S\in T$, we note $\eta_{S}$ the restriction of $\eta$ to $S$. We consider $\beta(S_1,S_2)$ the…
Mixture models are useful in a wide array of applications to identify subpopulations in noisy overlapping distributions. For example, in multiplexed immunofluorescence (mIF), cell image intensities represent expression levels and the cell…
Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference…
There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within…
We obtain a necessary and sufficient condition under which random-coefficient discrete choice models, such as mixed-logit models, are rich enough to approximate any nonparametric random utility models arbitrarily well across choice sets.…
In some contexts, mixture models can fit certain variables well at the expense of others in ways beyond the analyst's control. For example, when the data include some variables with non-trivial amounts of missing values, the mixture model…
We represent in this preprint the exact estimate for covariation berween two random variables (r.v.), which are measurable relative the corresponding sigma-algebras through anyhow mixing coefficients. We associate a solution of this problem…
Estimation of the $\phi$-divergence between two unknown probability distributions using empirical data is a fundamental problem in information theory and statistical learning. We consider a multi-variate generalization of the data dependent…
Finite mixture models are used in statistics and other disciplines, but inference for mixture models is challenging due, in part, to the multimodality of the likelihood function and the so-called label switching problem. We propose…