Related papers: Multiscale Methods for Shape Constraints in Deconv…
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…
There is a growing interest in cell-type-specific analysis from bulk samples with a mixture of different cell types. A critical first step in such analyses is the accurate estimation of cell-type proportions in a bulk sample. Although many…
We consider a multiplicative deconvolution problem, in which the density $f$ or the survival function $S^X$ of a strictly positive random variable $X$ is estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y =…
We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density.…
We propose a new testing procedure for detecting localized departures from monotonicity of a signal embedded in white noise. In fact, we perform simultaneously several tests that aim at detecting departures from concavity for the integrated…
We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…
Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
Image classification models tend to make decisions based on peripheral attributes of data items that have strong correlation with a target variable (i.e., dataset bias). These biased models suffer from the poor generalization capability…
We consider the problem of estimating a spatially varying density function, motivated by problems that arise in large-scale radiological survey and anomaly detection. In this context, the density functions to be estimated are the background…
We study the problem of parameter estimation for the homogenization limit of multiscale systems involving fractional dynamics. In the case of stochastic multiscale systems driven by Brownian motion, it has been shown that in order for the…
We propose tests for the convexity/linearity/concavity of a transformation of the dependent variable in a semiparametric transformation model. These tests can be used to verify monotonicity of the treatment effect, or, equivalently,…
We study the estimation of the invariant density of additive fractional stochastic differential equations with Hurst parameter $H \in (0,1)$. We first focus on continuous observations and develop a kernel-based estimator achieving faster…
Differential equations may possess coefficients that vary on a spectrum of scales. Because coefficients are typically multiplicative in real space, they turn into convolution operators in spectral space, mixing all wavenumbers. However, in…
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…
In the framework of shape constrained estimation, we review methods and works done in convex set estimation. These methods mostly build on stochastic and convex geometry, empirical process theory, functional analysis, linear programming,…
The density deconvolution problem involves recovering a target density g from a sample that has been corrupted by noise. From the perspective of Le Cam's local asymptotic normality theory, we show that non-parametric density deconvolution…
In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…
In medical research, often, genomic or proteomic data are collected, with measurements frequently subject to uncertainties or errors, making it crucial to accurately separate the signals of the genes or proteins, respectively, from the…
Electronic nearsightedness is one of the fundamental principles governing the behavior of condensed matter and supporting its description in terms of local entities such as chemical bonds. Locality also underlies the tremendous success of…