New bootstrap confidence intervals for means of positively skewed distributions

Santu Ghosh, Alan M. Polansky

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)6915-6927
Number of pages13
JournalCommunications in Statistics - Theory and Methods
Volume45
Issue number23
DOIs
StatePublished - Dec 1 2016

Keywords

  • Bandwidth parameter
  • Bootstrap percentile method
  • Bootstrap percentile-t method
  • Confidence interval

ASJC Scopus subject areas

  • Statistics and Probability

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