Almost sure convergence of bootstrapped means and \(U\)-statistics

DOI10.1016/0378-3758(94)90151-1zbMath0805.62049OpenAlexW2041359961MaRDI QIDQ1333117

Thomas Mikosch

Publication date: 6 February 1995

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-3758(94)90151-1

zbMATH Keywords

strong law of large numbersresamplinglaw of the iterated logarithmBorel-Cantelli lemmacentral limit theoremalmost sure convergencetailsempirical distributionbackward martingalesmoment conditionsfinite variancebootstrapped sample meansKolmogorov-type exponential inequalitiesMarcinkiewicz-Zygmund-type SLLNmultiple bootstrapsU-statistics of order 2

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric statistical resampling methods (62G09) Strong limit theorems (60F15)

Related Items (9)

A central limit theorem for bootstrap sample sums from non-i.i.d. models ⋮ General Weak Laws of Large Numbers for Bootstrap Sample Means ⋮ Large and moderate deviation principles for the bootstrap sample quantile ⋮ Rates in the complete convergence of bootstrap means. ⋮ A large deviation principle for bootstrapped sample means ⋮ Almost sure lim sup behavior of bootstrapped means with applications to pairwise i. i. d. sequences and stationary ergodic sequences ⋮ Complete convergence of bootstrapped means and moments of the supremum of normed bootstrapped sums ⋮ Asymptotic probability for the bootstrapped means deviations from the sample mean ⋮ Almost Sure lim sup Behavior of Dependent Bootstrap Means

Cites Work

• The contribution to the sum of the summand of maximum modulus
• Asymptotic properties of the bootstrap for heavy-tailed distributions
• Laws of large numbers for bootstrapped U-statistics
• Strong law for the bootstrap
• Limit theorems for methods of summation of independent random variables. I
• Random quadratic forms and the bootstrap for \(U\)-statistics
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