Cramér type moderate deviation theorems for self-normalized processes
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Publication:726728
DOI10.3150/15-BEJ719zbMath1350.60025arXiv1405.1218OpenAlexW1813834019MaRDI QIDQ726728
Publication date: 14 July 2016
Published in: Bernoulli (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1405.1218
moderate deviationsnormal approximation\(U\)-statisticsstudentized statisticsnonlinear statisticsrelative errorsself-normalized processes
Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Large deviations (60F10)
Related Items (13)
Refined Cramér-type moderate deviation theorems for general self-normalized sums with applications to dependent random variables and winsorized mean ⋮ Central limit theorem and self-normalized Cramér-type moderate deviation for Euler-Maruyama scheme ⋮ Berry-Esseen bounds for multivariate nonlinear statistics with applications to M-estimators and stochastic gradient descent algorithms ⋮ Tail bounds for empirically standardized sums ⋮ Self-normalization: taming a wild population in a heavy-tailed world ⋮ A refined randomized concentration inequality ⋮ Deviation inequalities and Cramér-type moderate deviations for the explosive autoregressive process ⋮ Cramér-type moderate deviations under local dependence ⋮ Cramér's type results for some bootstrapped \(U\)-statistics ⋮ High-dimensional consistent independence testing with maxima of rank correlations ⋮ Self-normalized Cramér type moderate deviations for martingales ⋮ Berry-Esseen bounds for generalized \(U\)-statistics ⋮ Cramér-type moderate deviations for the log-likelihood ratio of inhomogeneous Ornstein-Uhlenbeck processes
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