Estimating kurtosis and confidence intervals for the variance under nonnormality

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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)
JournalJournal of Statistical Computation and Simulation
DOIs
StateAccepted/In press - 2013

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Keywords

  • bootstrap
  • interval estimation
  • large-sample theory

ASJC Scopus subject areas

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

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