Main Article Content
This paper proposes a double bootstrap-t one-sided confidence interval for population variance of skewed distributions. The upper endpoint and lower endpoint confidence intervals are studied. The one-sided confidence intervals based on the chi-square statistic, bootstrap-t method and double bootstrap-t method are compared via Monte Carlo simulations. The simulation results indicated that the coverage probabilities of bootstrap-t confidence interval can be increased by using double bootstrap resampling. The upper endpoint confidence interval using double bootstrap-t method predominates the other methods with respect to the coverage probability criteria. The performance of the proposed one-sided confidence interval is illustrated with an empirical example.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Casella, G. and Berger, R. L. (2001). Statistical Inference. Duxbury Press, Pacific Grove, pp.257.
Cojbasic, V. and Loncar, D. (2011). One-sided confidence intervals for population variances of skewed distribution. Journal of Statistical Planning and Inference, 141(5): 1667-1672.
Cojbasic, V. and Tomovic, A. (2007). Nonparametric confidence intervals for population variances of one sample and the difference of variances of two samples. Computational Statistics & Data Analysis, 51(12): 5562-5578.
Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7(1): 1-26.
Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman & Hall, New York.
Hall, P. (1986). On the bootstrap and confidence intervals. Annals of Statistics, 14(4): 1431-1452.
Ihaka, R. and Gentleman, R. (1996). “R: A Language for Data Analysis and Graphics.” Journal of Computational and Graphical Statistics, 5: 299-314.
Nankervis, J. C. (2002). Stopping rules for double bootstrap confidence intervals, [Online URL: www.citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.86.8480&rep=rep1&type=pdf] accessed on November 19, 2012.
Nankervis, J. C. (2005). Computational algorithms for double bootstrap confidence intervals. Computational Statistics & Data Analysis, 49(2): 461-475.
Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supported to have arisen from random sampling. Philosophical Magazine, 50(5): 157-175.
Scherer, B. and Martin, R. D. (2005). Introduction to Modern Portfolio Optimization with NUOPT and S-PLUS. Springer, New York.
Tosasukul, J., Budsaba, K., and Volodin, A. (2009). Dependent bootstrap confidence intervals for a population mean. Thailand Statistician, 7(1): 43-51.