Strong consistencies of the bootstrap moments

Tien-Chung Hu

International Journal of Mathematics and Mathematical Sciences, 1991, vol. 14, 1-6

Abstract:

Let X be a real valued random variable with E | X | r + δ < ∞ for some positive integer r and real number, δ , 0 < δ ≤ r , and let { X , X 1 , X 2 , … } be a sequence of independent, identically distributed random variables. In this note, we prove that, for almost all w ∈ Ω , μ r ; n * ( w ) → μ r with probability 1 . if lim n → ∞ inf m ( n ) n − β > 0 for some β > r − δ r + δ , where μ r ; n * is the bootstrap r t h sample moment of the bootstrap sample some with sample size m ( n ) from the data set { X , X 1 , … , X n } and μ r is the r t h moment of X . The results obtained here not only improve on those of Athreya [3] but also the proof is more elementary.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:710517

DOI: 10.1155/S0161171291001060

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