Estimating kurtosis and confidence intervals for the variance under nonnormality

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

Exact confidence intervals for variances rely on normal distribution assumptions. Alternatively, large sample confidence intervals for the variance can be attained if one estimates the kurtosis of the underlying distribution. The method used to estimate the kurtosis has a direct impact on the performance of the interval and thus the quality of statistical inferences. In this paper the author considers a number of kurtosis estimators combined with large-sample theory to construct approximate confidence intervals for the variance. In addition, a nonparametric bootstrap resampling procedure is used to build bootstrap confidence intervals for the variance. Simulated coverage probabilities using different confidence interval methods are computed for a variety of sample sizes and distributions. A modification to a conventional estimator of the kurtosis, in conjunction with adjustments to the mean and variance of the asymptotic distribution of a function of the sample variance, improves the resulting coverage values for leptokurtically distributed populations.

Original languageEnglish (US)
Pages (from-to)2710-2720
Number of pages11
JournalJournal of Statistical Computation and Simulation
Volume84
Issue number12
DOIs
StatePublished - Jan 1 2014

Keywords

  • Bootstrap
  • Interval estimation
  • Large-sample theory

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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