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Estimating the Correlation Coefficients in a Multivariate Skew Normal Population Using the a Priori Procedure (APP)

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Financial Econometrics: Bayesian Analysis, Quantum Uncertainty, and Related Topics (ECONVN 2022)

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 427))

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Abstract

This paper expands the a priori procedure (APP) to enable researchers to determine appropriate sample sizes for using sample correlation coefficients to estimate corresponding population correlation coefficients. The underlying assumption is that the population follows a skew normal distribution, which is more general than the typical assumption of a normal distribution. Furthermore, we work out the statistical implications and provide links to free and user-friendly programs.

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References

  • Azzalini, A.: A class of distributions which includes the normal ones. Scandinavian J. Stat. 171–178 (1985)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Azzalini, A., Capitanio, A.: Statistical application of the multivariate skew normal distribution. J. Roy. Statist. Soc. B 83, 579–602 (1999)

    Google Scholar 

  • Anderson, T. W.: An Introduction to Multivariate Statistical Analysis–3rd ed. Wiley series in probability and mathematical statistics, ISBN 0-471-36091-0

    Google Scholar 

  • Olsson, U.: Maximum likelihood estimation of polychoric correlation coefficient. PSYCHOMETRIKA 44(4) (1979)

    Google Scholar 

  • Schisterman, E.F., Moysich, K.B., England, L.J. , Rao, M.: Estimation of the correlation coefficient using the Bayesian Approach and its applications for epidemiological research. BMC Med. Res. Methodol. 3:5 (2003)

    Google Scholar 

  • Shevlyakov, G., Smirnov, P.: Robust estimation of the correlation coefficient: an attempt of survey. Aust. J. Stat. 40(1 & 2), 147–156 (2011)

    Google Scholar 

  • Sari, B.G., Lúcio, A.D., Santana, C.S., Krysczun, D.K., Tischler, A.L., Drebes, L.: Sample size for estimation of the Pearson correlation coefficient in cherry tomato tests. Ciência Rural, Santa Maria, v.47: 10, e20170116 (2017)

    Google Scholar 

  • Wang, C., Wang, T., Trafimow, T, Zhang, X.: Necessary sample size for estimating the scale parameter with specified closeness and confidence. Int. J. Intell. Technol. Appl. Stat. 12(1), 17–29 (2019). https://doi.org/10.6148/IJITAS.201903_12(1).0002

  • Wang, C., Wang, T., Trafimow, D., Myuz, H.: Desired sample size for estimating the skewness parameter under skew normal settings. In: Kreinovich, V., Sriboonchitta, S. (eds.) Structural changes and their economic modeling. Springer-Verlag, Switzerland, pp. 152–162 (2019)

    Google Scholar 

  • Wang, C., Wang, T., Trafimow, D., Chen, J.: Extending a priori procedure to two independent samples under skew normal setting. Asian J. Econ. Bank. 03(02), 29-40 (2019)

    Google Scholar 

  • Wang, C., Wang, T., Trafimow, D., Li, H., Hu, L., Rodriguez, A.: Extending a priori procedure (APP) to address correlation coefficients. To appear In: Trung, N., Thach, N., Kreinovich, V. (eds.) Data science for financial econometrics. Springer-Verlag (2020)

    Google Scholar 

  • Wang, C., Wang, T., Trafimow, D., Myuz, H.A.: Necessary sample size for specified closeness and confidence of matched data under the skew normal setting. Commun. Stat. Simul. Comput. (2019). https://doi.org/10.1080/03610918.2019.1661473

    Article  MATH  Google Scholar 

  • Wang, Z., Wang, C., Wang, T.: Estimation of location parameter on the skew normal setting with known coefficient of variation and skewness. Int. J. Intell. Technol. Appl. Stat. 9(3), 45–63 (2016)

    Google Scholar 

  • Zhu, X., Li, B., Wang, T., Gupta, A.: Sampling distributions of skew normal populations associated with closed skew normal distributions. Random Oper. Stoch. Equ. 2019 (2019). https://doi.org/10.1515/rose-2018-2007

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Correspondence to Tonghui Wang .

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Wang, C., Wang, T., Trafimow, D., Tong, T. (2022). Estimating the Correlation Coefficients in a Multivariate Skew Normal Population Using the a Priori Procedure (APP). In: Ngoc Thach, N., Kreinovich, V., Ha, D.T., Trung, N.D. (eds) Financial Econometrics: Bayesian Analysis, Quantum Uncertainty, and Related Topics. ECONVN 2022. Studies in Systems, Decision and Control, vol 427. Springer, Cham. https://doi.org/10.1007/978-3-030-98689-6_11

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