Estimating kurtosis and confidence intervals for the variance under nonnormality

Research output: Contribution to journalArticle

6 Citations (Scopus)

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

Fingerprint

Non-normality
Kurtosis
Normal distribution
Confidence interval
Exact Confidence Interval
Nonparametric Bootstrap
Large Sample Theory
Bootstrap Confidence Intervals
Estimator
Sample variance
Interval Methods
Coverage Probability
Resampling
Statistical Inference
Estimate
Asymptotic distribution
Gaussian distribution
Adjustment
Sample Size
Coverage

Keywords

  • bootstrap
  • interval estimation
  • large-sample theory

ASJC Scopus subject areas

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

Cite this

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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.",
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