Bootstrap of the Mean in the Infinite Variance Case

Let X1, X2, ..., Xnbe independent identically distributed random variables with EX2 1= ∞ but X1belonging to the domain of attraction of a stable law. It is known that the sample mean X̄nappropriately normalized converges to a stable law. It is shown here that the bootstrap version of the normalized...

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Published in:The Annals of statistics 1987-06, Vol.15 (2), p.724-731
Main Author: Athreya, K. B.
Format: Article
Language:English
Subjects:
60F
62E
62F
Bootstrap
Distribution functions
Eigenfunctions
Exact sciences and technology
Mathematical vectors
Mathematics
Nonparametric inference
Perceptron convergence procedure
Poisson random measure
Probability and statistics
Random sampling
Random variables
Sample mean
Sciences and techniques of general use
stable law
Statistical distributions
Statistical variance
Statistics
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description Let X1, X2, ..., Xnbe independent identically distributed random variables with EX2 1= ∞ but X1belonging to the domain of attraction of a stable law. It is known that the sample mean X̄nappropriately normalized converges to a stable law. It is shown here that the bootstrap version of the normalized mean has a random distribution (given the sample) whose limit is also a random distribution implying that the naive bootstrap could fail in the heavy tailed case.
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subjects 60F
62E
62F
Bootstrap
Distribution functions
Eigenfunctions
Exact sciences and technology
Mathematical vectors
Mathematics
Nonparametric inference
Perceptron convergence procedure
Poisson random measure
Probability and statistics
Random sampling
Random variables
Sample mean
Sciences and techniques of general use
stable law
Statistical distributions
Statistical variance
Statistics
title Bootstrap of the Mean in the Infinite Variance Case
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