### 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 language | English (US) |
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Pages (from-to) | 1-20 |

Number of pages | 20 |

Journal | Statistical Methods and Applications |

DOIs | |

State | Accepted/In press - Jul 3 2017 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

**Distribution-dependent and distribution-free confidence intervals for the variance.** / Burch, Brent D.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Distribution-dependent and distribution-free confidence intervals for the variance

AU - Burch, Brent D

PY - 2017/7/3

Y1 - 2017/7/3

N2 - 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.

AB - 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.

KW - Bootstrap

KW - Coverage probability

KW - Interval estimation

KW - Large-sample theory

KW - Nonparametric

UR - http://www.scopus.com/inward/record.url?scp=85021777860&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021777860&partnerID=8YFLogxK

U2 - 10.1007/s10260-017-0385-z

DO - 10.1007/s10260-017-0385-z

M3 - Article

AN - SCOPUS:85021777860

SP - 1

EP - 20

JO - Statistical Methods and Applications

JF - Statistical Methods and Applications

SN - 1618-2510

ER -