Distribution-dependent and distribution-free confidence intervals for the variance

Research output: Contribution to journalArticle

Abstract

Finding an interval estimation procedure for the variance of a population that achieves a specified confidence level can be problematic. If the distribution of the population is known, then a distribution-dependent interval for the variance can be obtained by considering a power transformation of the sample variance. Simulation results suggest that this method produces intervals for the variance that maintain the nominal probability of coverage for a wide variety of distributions. If the underlying distribution is unknown, then the power itself must be estimated prior to forming the endpoints of the interval. The result is a distribution-free confidence interval estimator of the population variance. Simulation studies indicate that the power transformation method compares favorably to the logarithmic transformation method and the nonparametric bias-corrected and accelerated bootstrap method for moderately sized samples. However, two applications, one in forestry and the other in health sciences, demonstrate that no single method is best for all scenarios.

Original languageEnglish (US)
Pages (from-to)1-20
Number of pages20
JournalStatistical Methods and Applications
DOIs
StateAccepted/In press - Jul 3 2017

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Distribution-free
Confidence interval
Power Transformation
Dependent
Sample variance
Interval Methods
Forestry
Interval
Interval Estimation
Bootstrap Method
Confidence Level
Categorical or nominal
Logarithmic
Health
Coverage
Simulation Study
Estimator
Unknown
Scenarios
Demonstrate

Keywords

  • Bootstrap
  • Coverage probability
  • Interval estimation
  • Large-sample theory
  • Nonparametric

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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abstract = "Finding an interval estimation procedure for the variance of a population that achieves a specified confidence level can be problematic. If the distribution of the population is known, then a distribution-dependent interval for the variance can be obtained by considering a power transformation of the sample variance. Simulation results suggest that this method produces intervals for the variance that maintain the nominal probability of coverage for a wide variety of distributions. If the underlying distribution is unknown, then the power itself must be estimated prior to forming the endpoints of the interval. The result is a distribution-free confidence interval estimator of the population variance. Simulation studies indicate that the power transformation method compares favorably to the logarithmic transformation method and the nonparametric bias-corrected and accelerated bootstrap method for moderately sized samples. However, two applications, one in forestry and the other in health sciences, demonstrate that no single method is best for all scenarios.",
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