Dependent Bootstrap Confidence Intervals for a Population Mean

Authors

  • Jiraroj Tosasukul Department of Mathematics and Statistics, Thammasat University, Rangsit Center, Pathum Thani 12121, Thailand.
  • Kamon Budsaba Department of Mathematics and Statistics, Thammasat University, Rangsit Center, Pathum Thani 12121, Thailand.
  • Andrei Volodin Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada S4S 0A2

Keywords:

average interval lengths, Bootstrap-t method, coverage probabilities, dependent bootstrap procedure, independent bootstrap procedure, Modified Percentile method, Percentile method

Abstract

This study compares and analyzes the coverage probabilities and the average interval lengths of confidence interval for a population mean based on the dependent bootstrap procedure against those based on the independent bootstrap procedure.  Both dependent and independent bootstrap confidence intervals for a population mean are computed by the Bootstrap-t, Percentile, and Modified Percentile methods.  Simulations show that the coverage probabilities of the dependent bootstrap confidence intervals are similar to those of the independent bootstrap confidence intervals.  The average interval lengths of the dependent bootstrap method are shorter for most situations.  For both the independent and dependent bootstrap confidence intervals, the coverage probabilities increase and the average interval lengths decrease as the sample size n increase for Normal, Gamma, and Chi-square distributions, as well as three methods used in this work.

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How to Cite

Tosasukul, J., Budsaba, K., & Volodin, A. (2015). Dependent Bootstrap Confidence Intervals for a Population Mean. Thailand Statistician, 7(1), 43–51. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/34320

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Articles