Related papers: Optimal Demixing of Nonparametric Densities

This paper investigates the statistical estimation of a discrete mixing measure $\mu$0 involved in a kernel mixture model. Using some recent advances in l1-regularization over the space of measures, we introduce a "data fitting and…

Gaussian graphical models (GGMs) are widely used to recover the conditional independence structure among random variables. Recent work has sought to incorporate auxiliary covariates to improve estimation, particularly in applications such…

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…

While nonparametric density estimators often perform well on low dimensional data, their performance can suffer when applied to higher dimensional data, owing presumably to the curse of dimensionality. One technique for avoiding this is to…

We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…

Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…

Let $X_1,..., X_n$ be i.i.d.\ copies of a random variable $X=Y+Z,$ where $ X_i=Y_i+Z_i,$ and $Y_i$ and $Z_i$ are independent and have the same distribution as $Y$ and $Z,$ respectively. Assume that the random variables $Y_i$'s are…

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…

Nonparametric kernel density estimation is a very natural procedure which simply makes use of the smoothing power of the convolution operation. Yet, it performs poorly when the density of a positive variable is to be estimated (boundary…

Hyperspectral images provide much more information than conventional imaging techniques, allowing a precise identification of the materials in the observed scene, but because of the limited spatial resolution, the observations are usually…

The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…

The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…

A novel nonparametric clustering algorithm is proposed using the interpoint distances between the members of the data to reveal the inherent clustering structure existing in the given set of data, where we apply the classical nonparametric…

In a multiple testing context, we consider a semiparametric mixture model with two components where one component is known and corresponds to the distribution of $p$-values under the null hypothesis and the other component $f$ is…

We study the problem of estimating the probability density function of a circular random variable subject to censoring. To this end, we propose a fully computable quotient estimator that combines a projection estimator on linear sieves with…

We study non-parametric estimation of an unknown density with support in R (respectively R+). The proposed estimation procedure is based on the projection on finite dimensional subspaces spanned by the Hermite (respectively the Laguerre)…

This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The…

The major contributions of this paper lie in two aspects. Firstly, we focus on deriving Bernstein-type inequalities for both geometric and algebraic irregularly-spaced NED random fields, which contain time series as special case.…

Kernel-based nonparametric hazard rate estimation is considered with a special class of infinite-order kernels that achieves favorable bias and mean square error properties. A fully automatic and adaptive implementation of a density and…

This study focuses on statistical inference for compound models of the form $X=\xi_1+\ldots+\xi_N$, where $N$ is a random variable denoting the count of summands, which are independent and identically distributed (i.i.d.) random variables…