Moment inequalities for U-statistics
By Radosław Adamczak. 2005
66 citations recorded by the source corpus.
We present moment inequalities for completely degenerate Banach space valued (generalized) U-statistics of arbitrary order. The estimates involve suprema of empirical processes which, in the real-valued case, can be replaced by simpler norms of the kernel matrix (i.e., norms of some multilinear operators associated with the kernel matrix). As a corollary, we derive tail inequalities for U-statistics with bounded kernels and for some multiple stochastic integrals.
Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/b7f67ac438da793479a0395fc72344d0b5b9ce87
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In Applied Mathematics
- Gábor Lugosi
- H. Sambale
- St'ephan Cl'emenccon
- A. Sinulis
- Nicolas Vayatis
- Rafal Latala
- Friedrich Götze
- Emanuel Milman
In Mathematical Physics
- Friedrich Götze
- H. Sambale
- A. Sinulis
- St'ephan Cl'emenccon
- Nicolas Vayatis
- Gábor Lugosi
- Rafal Latala
- Radosław Adamczak
In Statistics and Probability
- Nicolas Vayatis
- H. Sambale
- St'ephan Cl'emenccon
- A. Sinulis
- Gábor Lugosi
- Rafal Latala
- Friedrich Götze
- Roman Vershynin
Citations in the corpus
- Ranking and empirical minimization of U-statistics (2006, background): “We point out here that the recent work of Adamczak [1] establishes very general moment inequalities for Banach space-valued degenerate U -statistics of arbitrary order.”
- Concentration inequalities for polynomials in α-sub-exponential random variables (2019, background): “The case of α ∈ [1, 2] and polynomials of total degree D ≤ 3 has been discussed in [4, Proposition 6.”
- Estimates of moments and tails of Gaussian chaoses (2005, background): “ij aijg (1) i g (2) j ∥∥∥∥ p ∼p‖(aij)‖{1,2} + p‖(aij)‖{1}{2}, (2)”