
Robust Density Estimation under Besov IPM Losses
We study minimax convergence rates of nonparametric density estimation i...
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Minimax and adaptive tests for detecting abrupt and possibly transitory changes in a Poisson process
Motivated by applications in cybersecurity and epidemiology, we consider...
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Minimax Optimal Conditional Density Estimation under Total Variation Smoothness
This paper studies the minimax rate of nonparametric conditional density...
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Density estimation on an unknown submanifold
We investigate density estimation from a nsample in the Euclidean space...
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Cytometry inference through adaptive atomic deconvolution
In this paper we consider a statistical estimation problem known as atom...
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Minimax Rates for Conditional Density Estimation via Empirical Entropy
We consider the task of estimating a conditional density using i.i.d. sa...
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What is resolution? A statistical minimax testing perspective on superresolution microscopy
As a general rule of thumb the resolution of a light microscope (i.e. th...
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Dispersal density estimation across scales
We consider a space structured population model generated by two point clouds: a homogeneous Poisson process M=∑_jδ_X_j with intensity of order n→∞ as a model for a parent generation together with a Cox point process N=∑_jδ_Y_j as offspring generation, with conditional intensity of order M∗(σ^1f(·/σ)), where ∗ denotes convolution, f is the socalled dispersal density, the unknown parameter of interest, and σ>0 is a physical scale parameter. Based on a realisation of M and N, we study the nonparametric estimation of f, for several regimes σ=σ_n. We establish that the optimal rates of convergence do not depend monotonously on the scale σ and construct minimax estimators accordingly. Depending on σ, the reconstruction problem exhibits a competition between a direct and a deconvolution problem. Our study reveals in particular the existence of a least favourable intermediate inference scale.
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