### 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 language | English (US) |
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Journal | Journal of Statistical Computation and Simulation |

DOIs | |

State | Accepted/In press - 2013 |

### Fingerprint

### 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

**Estimating kurtosis and confidence intervals for the variance under nonnormality.** / Burch, Brent D.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Estimating kurtosis and confidence intervals for the variance under nonnormality

AU - Burch, Brent D

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - bootstrap

KW - interval estimation

KW - large-sample theory

UR - http://www.scopus.com/inward/record.url?scp=84884570227&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884570227&partnerID=8YFLogxK

U2 - 10.1080/00949655.2013.840628

DO - 10.1080/00949655.2013.840628

M3 - Article

AN - SCOPUS:84884570227

JO - Journal of Statistical Computation and Simulation

JF - Journal of Statistical Computation and Simulation

SN - 0094-9655

ER -