This tutorial provides a gentle introduction to kernel density estimation (KDE) and recent
advances regarding confidence bands and geometric/topological features. We begin with a …

Many modern methods for prediction leverage nearest neighbor search to find past training
examples most similar to a test example, an idea that dates back in text to at least the 11th …

We address the problem of density estimation with" L_s-loss by selection of kernel
estimators. We develop a selection procedure and derive corresponding L_s-risk oracle …

We consider a system of N interacting particles, governed by transport and diffusion, that
converges in a mean-field limit to the solution of a McKean–Vlasov equation. From the …

Estimator selection has become a crucial issue in non parametric estimation. Two widely
used methods are penalized empirical risk minimization (such as penalized log-likelihood …

Sharp oracle inequalities for aggregation of affine estimators Page 1 The Annals of Statistics
2012, Vol. 40, No. 4, 2327–2355 DOI: 10.1214/12-AOS1038 © Institute of Mathematical …

This paper is concerned by statistical inference problems from a data set whose elements
may be modeled as random probability measures such as multiple histograms or point …

This paper investigates the bias and the weak Bahadur representation of a local polynomial
estimator of the conditional quantile function and its derivatives. The bias and Bahadur …

We study a multivariate version of trend filtering, called Kronecker trend filtering or KTF, for
the case in which the design points form a lattice in $ d $ dimensions. KTF is a natural …

Consider some multivariate diffusion process X=(X t) t≥ 0 with unique invariant probability
measure and associated invariant density ρ, and assume that a continuous record of …