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We consider here estimation of an unknown probability density s belonging to L2(mu) where mu is a probability measure. We have at hand n i.i.d. observations with density s and use the squared L2-norm as our loss function. The purpose of…

In this work, we use the Belief Function Theory which extends the probabilistic framework in order to provide uncertainty bounds to different categories of crowd density estimators. Our method allows us to compare the multi-scale…

Non-parametric estimation of a multivariate density estimation is tackled via a method which combines traditional local smoothing with a form of global smoothing but without imposing a rigid structure. Simulation work delivers encouraging…

Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…

We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…

In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…

We investigate the estimation of a weighted density taking the form $g=w(F)f$, where $f$ denotes an unknown density, $F$ the associated distribution function and $w$ is a known (non-negative) weight. Such a class encompasses many examples,…

Functional data analysis is proved to be useful in many scientific applications. The physical process is observed as curves and often there are several curves observed due to multiple subjects, providing the replicates in statistical sense.…

This paper concerns estimating a probability density function $f$ based on iid observations from $g(x)=W^{-1} w(x) f(x)$, where the weight function $w$ and the total weight $W=\int w(x) f(x) dx$ may not be known. The length-biased and…

In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…

Density level sets are mainly estimated using one of three methodologies: plug-in, excess mass, or a hybrid approach. The plug-in methods are based on replacing the unknown density by some nonparametric estimator, usually the kernel. Thus,…

This paper focuses on the problem of unbounded density ratio estimation -- an understudied yet critical challenge in statistical learning -- and its application to covariate shift adaptation. Much of the existing literature assumes that the…

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…

In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…

Multivariate density estimation is a popular technique in statistics with wide applications including regression models allowing for heteroskedasticity in conditional variances. The estimation problems become more challenging when…

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…

Uncertainty estimation is essential to make neural networks trustworthy in real-world applications. Extensive research efforts have been made to quantify and reduce predictive uncertainty. However, most existing works are designed for…

We consider the problem of multivariate density estimation when the unknown density is assumed to follow a particular form of dimensionality reduction, a noisy independent factor analysis (IFA) model. In this model the data are generated by…

In this paper we focus on a type of inverse problem in which the data is expressed as an unknown function of the sought and unknown model function (or its discretised representation as a model parameter vector). In particular, we deal with…

The density ratio is an important metric for evaluating the relative likelihood of two probability distributions, with extensive applications in statistics and machine learning. However, existing estimation theories for density ratios often…