Skip to main content

Estimating the location parameter under skew normal settings: is violating the independence assumption good or bad?

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Researchers typically assume that they are working from a normal distribution and with independent sampling. Both assumptions are often violated. Our goal was to explore the intersection of the violations: Is the net effect good or bad? Using the family of skew-normal distributions, which is a superset of the family of normal distributions, we tested whether the mean squared error (MSE) is less under dependence or under independence. We found that the MSE is less under dependence, under the assumption that elements in both samples are identically distributed related to the population distribution. In addition, increasing skewness and increasing sample size also decrease the MSE. Finally, the largest differences in MSE between dependence and independence occur under moderate skewness.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Notes

  1. In probability theory and statistics, the moment generating function of a real-valued random variable (or vector) is an alternative specification of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.

References

Download references

Acknowledgements

Authors would like to thank Dr. Z. Wei (University of Maine) and Dr. R. Steiner (New Mexico State University) for their comments, which lead to the improvement of this paper.

Funding

This work was not supported by any funding source.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tonghui Wang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Communicated by Vladik Kreinovich.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, C., Wang, T., Trafimow, D. et al. Estimating the location parameter under skew normal settings: is violating the independence assumption good or bad?. Soft Comput 25, 7795–7802 (2021). https://doi.org/10.1007/s00500-021-05679-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-021-05679-4

Keywords