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Plausibility Regions on the Skewness Parameter of Skew Normal Distributions Based on Inferential Models

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Robustness in Econometrics

Part of the book series: Studies in Computational Intelligence ((SCI,volume 692))

Abstract

Inferential models (IMs) are new methods of statistical inference. They have several advantages: (1) They are free of prior distributions; (2) They rely on data. In this paper, \(100(1-\alpha )\%\) plausibility regions of the skewness parameter of skew-normal distributions are constructed by using IMs, which are the counterparts of classical confidence intervals in IMs.

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References

  1. Aronld BC, Beaver RJ, Groenevld RA, Meeker WQ (1993) The nontruncated marginal of a truncated bivariate normal distribution. Psychometrica 58(3):471–488

    Article  MathSciNet  MATH  Google Scholar 

  2. Azzalini A (1985) A class of distributions which includes the normal ones. Scand J Stat 12(2):171–178

    MathSciNet  MATH  Google Scholar 

  3. Azzalini A (1986) Further results on a class of distributions which includes the normal ones. Statistica 46(2):199–208

    MathSciNet  MATH  Google Scholar 

  4. Azzalini A, Capitanio A (1999) Statistical applications of the multivariate skew normal distribution. J R Stat Soc 61(3):579–602

    Article  MathSciNet  MATH  Google Scholar 

  5. Azzalini A, Capitanio A (2013) The skew-normal and related families, vol 3. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  6. Azzalini A, Dalla Valle A (1996) The multivariate skew-normal distribution. Biometrika 83(4):715–726

    Article  MathSciNet  MATH  Google Scholar 

  7. Dey D (2010) Estimation of the parameters of skew normal distribution by approximating the ratio of the normal density and distribution functions. PhD thesis, University of California Riverside

    Google Scholar 

  8. Hill M, Dixon WJ (1982) Robustness in real life: a study of clinical laboratory data. Biometrics 38:377–396

    Article  Google Scholar 

  9. Liseo B, Loperfido N (2006) A note on reference priors for the scalar skew-normal distribution. J Stat Plan Inference 136(2):373–389

    Article  MathSciNet  MATH  Google Scholar 

  10. Martin R, Liu C (2013) Inferential models: a framework for prior-free posterior probabilistic inference. J Am Stat Assoc 108(501):301–313

    Article  MathSciNet  MATH  Google Scholar 

  11. Martin R (2014) Random sets and exact confidence regions. Sankhya A 76(2):288–304

    Article  MathSciNet  MATH  Google Scholar 

  12. Martin R, Liu C (2015) Inferential models: reasoning with uncertainty, vol 145. CRC Press, New York

    Google Scholar 

  13. Martin R, Lingham RT (2016) Prior-free probabilistic prediction of future observations. Technometrics 58(2):225–235

    Article  MathSciNet  Google Scholar 

  14. Mameli V, Musio M, Sauleau E, Biggeri A (2012) Large sample confidence intervals for the skewness parameter of the skew-normal distribution based on Fisher’s transformation. J Appl Stat 39(8):1693–1702

    Article  MathSciNet  MATH  Google Scholar 

  15. Sartori N (2006) Bias prevention of maximum likelihood estimates for scalar skew-normal and skew-t distributions. J Stat Plan Inference 136(12):4259–4275

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang T, Li B, Gupta AK (2009) Distribution of quadratic forms under skew normal settings. J Multivar Anal 100(3):533–545

    Article  MathSciNet  MATH  Google Scholar 

  17. Ye R, Wang T, Gupta AK (2014) Distribution of matrix quadratic forms under skew-normal settings. J Multivar Anal 131:229–239

    Article  MathSciNet  MATH  Google Scholar 

  18. Ye R, Wang T (2015) Inferences in linear mixed models with skew-normal random effects. Acta Mathematica Sinica, English Series 31(4):576–594

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to thank referees for their valuable comments.

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Correspondence to Tonghui Wang .

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Appendix

Appendix

Table 4 The observed values of LAI

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Zhu, X., Ma, Z., Wang, T., Teetranont, T. (2017). Plausibility Regions on the Skewness Parameter of Skew Normal Distributions Based on Inferential Models. In: Kreinovich, V., Sriboonchitta, S., Huynh, VN. (eds) Robustness in Econometrics. Studies in Computational Intelligence, vol 692. Springer, Cham. https://doi.org/10.1007/978-3-319-50742-2_16

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  • DOI: https://doi.org/10.1007/978-3-319-50742-2_16

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  • Online ISBN: 978-3-319-50742-2

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