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New bootstrap confidence intervals for means of positively skewed distributions

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  • Santu Ghosh
  • Alan M. Polansky

Abstract

In this paper, we consider the problem of constructing non parametric confidence intervals for the mean of a positively skewed distribution. We suggest calibrated, smoothed bootstrap upper and lower percentile confidence intervals. For the theoretical properties, we show that the proposed one-sided confidence intervals have coverage probability α + O(n− 3/2). This is an improvement upon the traditional bootstrap confidence intervals in terms of coverage probability. A version smoothed approach is also considered for constructing a two-sided confidence interval and its theoretical properties are also studied. A simulation study is performed to illustrate the performance of our confidence interval methods. We then apply the methods to a real data set.

Suggested Citation

  • Santu Ghosh & Alan M. Polansky, 2016. "New bootstrap confidence intervals for means of positively skewed distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(23), pages 6915-6927, December.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:23:p:6915-6927
    DOI: 10.1080/03610926.2014.972569
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