A law of the single logarithm for weighted sums of arrays applied to bootstrap model selection in regression

DOI10.1016/J.SPL.2012.01.018zbMath1321.62036OpenAlexW2001684823MaRDI QIDQ433587

Christian Léger, Pierre Lafaye de Micheaux

Publication date: 5 July 2012

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2012.01.018

zbMATH Keywords

linear regressionvariable selectionBICtriangular arraysrowwise independent

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Nonparametric statistical resampling methods (62G09) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Uses Software

• bootstrap

Cites Work

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• Iterated logarithm type behavior for weighted sums of i.i.d. random variables
• A law of the single logarithm for weighted sums of i.i.d. random elements
• A law of the iterated logarithm for double arrays of independent random variables with applications to regression and time series models
• Estimating the dimension of a model
• A strongly consistent procedure for model selection in a regression problem
• On the rate of convergence in the strong law of large numbers for arrays
• Asymptotic Statistics
• On strong convergence of arrays
• Probability for Statisticians
• A Strong Law for B-Valued Arrays
• Almost sure lim sup behavior of bootstrapped means with applications to pairwise i. i. d. sequences and stationary ergodic sequences

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