Abstract
In this paper, plausibility functions and \(100(1-\alpha )\%\) plausibility regions on location parameter and scale parameter of skew normal distributions are obtained in several cases by using inferential models (IMs), which are new methods of statistical inference. Simulation studies and one real data example are given for illustration of our results.
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References
Azzalini, A.: A class of distributions which includes the normal ones. Scand. J. Stat. 12(2), 171–178 (1985)
Azzalini, A.: The Skew-Normal and Related Families, vol. 3. Cambridge University Press, Cambridge (2013)
Azzalini, A., Capitanio, A.: Statistical applications of the multivariate skew normal distribution. J. R. Stat. Soc. 61(3), 579–602 (1999)
Azzalini, A., Dalla, V.A.: The multivariate skew-normal distribution. Biometrika 83(4), 715–726 (1996)
González-Farías, G., Domínguez-Molina, A., Gupta, A.K.: Additive properties of skew normal random vectors. J. Stat. Plan. Infer. 126(2), 521–534 (2004)
Martin, R.: Random sets and exact confidence regions. Sankhya A 76(2), 288–304 (2014)
Martin, R., Lingham, R.T.: Prior-free probabilistic prediction of future observations. Technometrics 58(2), 225–235 (2016)
Martin, R., Liu, C.: Inferential models: a framework for prior-free posterior probabilistic inference. J. Am. Stat. Assoc. 108(501), 301–313 (2013)
Martin, R., Liu, C.: Inferential Models: Reasoning with Uncertainty, vol. 145. CRC Press, New York (2015)
Tian, W., Wang, T.: Quadratic forms of refined skew normal models based on stochastic representation. Random Oper. Stochast. Equ. 24(4), 225–234 (2016)
Wang, T., Li, B., Gupta, A.K.: Distribution of quadratic forms under skew normal settings. J. Multivar. Anal. 100(3), 533–545 (2009)
Wang, Z., Wang, C., Wang, T.: Estimation of location parameter in the skew normal setting with known coefficient of variation and skewness. Int. J. Intell. Technol. Appl. Stat. 9(3), 191–208 (2016)
Ye, R., Wang, T.: Inferences in linear mixed models with skew-normal random effects. Acta Math. Sin. English Ser. 31(4), 576–594 (2015)
Ye, R., Wang, T., Gupta, A.K.: Distribution of matrix quadratic forms under skew-normal settings. J. Multivar. Anal. 131, 229–239 (2014)
Zhu, X., Ma, Z., Wang, T., Teetranont, T.: Plausibility regions on the skewness parameter of skew normal distributions based on inferential models. In: Robustness in Econometrics, pp. 267–286. Springer (2017)
Acknowledgments
We would like to thank Professor Hung T. Nguyen for introducing this interesting topic to us and referees for their valuable comments and suggestions which improve this paper.
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Zhu, X., Li, B., Wu, M., Wang, T. (2018). Plausibility Regions on Parameters of the Skew Normal Distribution Based on Inferential Models. In: Kreinovich, V., Sriboonchitta, S., Chakpitak, N. (eds) Predictive Econometrics and Big Data. TES 2018. Studies in Computational Intelligence, vol 753. Springer, Cham. https://doi.org/10.1007/978-3-319-70942-0_21
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DOI: https://doi.org/10.1007/978-3-319-70942-0_21
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