Accuracy of the bootstrap approximation

Arup Bose, G. Jogesh Babu

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The sampling distribution of several commonly occurring statistics are known to be closer to the corresponding bootstrap distribution than the normal distribution, under some conditions on the moments and the smoothness of the population distribution. These conditional approximations are suggestive of the unconditional ones considered in this paper, though one cannot be derived from the other by elementary methods. In this paper, probabilistic bounds are provided for the deviation of the sampling distribution from the bootstrap distribution. The rate of convergence to one, of the probability that the bootstrap approximation outperforms the normal approximation, is obtained. These rates can be applied to obtain the Lp bounds of Bhattacharya and Qumsiyeh (1989) under weaker conditions. The results apply to studentized versions of functions of multivariate means and thus cover a wide class of common statistics. As a consequence we also obtain approximations to percentiles of studentized means and their appropriate modifications. The results indicate the accuracy of the bootstrap confidence intervals both in terms of the actual coverage probability achieved and also the limits of the confidence interval.

Original languageEnglish (US)
Pages (from-to)301-316
Number of pages16
JournalProbability Theory and Related Fields
Volume90
Issue number3
DOIs
StatePublished - Sep 1 1991

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Bootstrap
Sampling Distribution
Approximation
Statistics
Bootstrap Confidence Intervals
Normal Approximation
Percentile
Coverage Probability
Confidence interval
Gaussian distribution
Smoothness
Rate of Convergence
Deviation
Cover
Moment
Sampling
Class

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Analysis
  • Mathematics(all)

Cite this

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Accuracy of the bootstrap approximation. / Bose, Arup; Babu, G. Jogesh.

In: Probability Theory and Related Fields, Vol. 90, No. 3, 01.09.1991, p. 301-316.

Research output: Contribution to journalArticle

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