Adaptive minimax multivariate $L^1$-deconvolution: harmonic-mean rates under noise filtering, and a $1$-Wasserstein equivalence NBNERWXW53

Expressions

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
Minimax optimality of the projection estimator for $\We$ on \(\mathcal P_{\text{prod}}\	statement	theorem 8.2	arxiv
Talagrand's inequality	statement	lemma S12.1	arxiv
Upper bound on the stochastic error	statement	proposition S4.2	arxiv
Upper bound on the $L^1$-risk of $\widehat F_{n,\mathbf{h}}^\ast$	statement	theorem 4.3	arxiv
Lower bound on the minimax $L^1$-risk	statement	theorem 5.1	arxiv
4HVR69361N	statement	lemma S10.1	arxiv
Concentration inequality for the $L^2$-error of $\widehat F_{n,\mathbf{h}}$	statement	proposition S12.2	arxiv
Rate preservation under compact support restriction	statement	corollary S13.2	arxiv
DR0Q5P02CX	statement	lemma S11.2	arxiv
Oracle inequality	statement	theorem 7.1	arxiv
First-order expansion of a perturbed product	statement	lemma S11.3	arxiv
Finite first moment of the integrated estimator	statement	lemma S13.1	arxiv
Anisotropic Nikol'skii class of densities	definition	definition S2.1	arxiv
N3KEBFK4P0	definition	definition S11.1	arxiv
Unbiasedness of the estimator $\widehat F_{n,\mathbf{H}}(\mathbf{x})$	statement	proposition S3.1	arxiv
Product class with finite first moment	definition	definition S8.1	arxiv
Unified oracle inequalities for $L^1$- and $L^2$-norms	statement	theorem 7.2	arxiv
Upper bound on the $L^1$-bias for anisotropic Nikol'skii classes	statement	proposition S4.1	arxiv
Existence of a superkernel	statement	proposition S4.6	arxiv
ZJ5JY3HKFZ	statement	theorem 4.4	arxiv
Superkernel	definition	definition S4.5	arxiv