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Forskningsartikel, 2003

Necessary and Sufficient Conditions for Consistency of Resampling

Belyaev, Yuri


A triangular array of independent non-identically distributed random variables is considered. The distribution functions of centered and rescaled sums of the random variables are estimated by resampling from the lists of their observed values. The estimators of distributions are called consistent (in probability) if they are weakly approaching the estimated distributions in probability, as the number of observations increases to infinity. Under some additional assumptions this type of consistency implies convergence in several metrics, e.g. in the uniform metric. A necessary and sufficient condition for consistency is given. In addition a new formulation of the Central Limit Theorem for triangular arrays, related to the notion of weakly approaching distribution functions, is stated. These results can be applied to justify the possibility of using resampling (bootstrap) techniques in many statistical applications, e.g. to justify the method of resampling from the list of weighted residuals in the case of a linear heteroscedastic regression


Triangular array; non-identically distributed random variables; central limit theorem; resampling; consistent estimation of distribution functions

Publicerad i

Research report (Centre of Biostochastics)
2003, Volym: 2003, nummer: 1, sidor: 1-26
Utgivare: SLU

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