Constructing the nonlinear regression equations based on multivariate normalizing transformations
Keywords:
non-linear regression equation, confidence interval, prediction interval, normalizing transformation, multivariate non-Gaussian data
Abstract
In the paper we consider the techniques to construct the equations, confidence and prediction intervals of nonlinear regressions on the basis of multivariate normalizing transformations for non-Gaussian data. We demonstrate that the poor normalization of multivariate non-Gaussian data using the univariate transformations leads to an expansion of the confidence and prediction intervals of non-linear regression for a larger number of data rows compared to the multivariate normalizing transformation.
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References
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2. G. A. F. Seber, and C. J. Wild, Nonlinear Regression. New York: John Wiley & Sons, 1989. DOI: 10.1002/0471725315
3. T. P. Ryan, Modern regression methods. New York: John Wiley & Sons, 1997. DOI: 10.1002/9780470382806
4. R. A. Johnson, and D. W. Wichern, Applied Multivariate Statistical Analysis. Pearson Prentice Hall, 2007.
5. S. B. Prykhodko, “Developing the software defect prediction models using regression analysis based on normalizing transformations” in “Modern problems in testing of the applied software” (PTASS-2016), Abstracts of the Research and Practice Seminar, Poltava, Ukraine, May 25-26, 2016, pp. 6-7.
6. Hee Beng Kuan Tan, Yuan Zhao, and Hongyu Zhang, “Estimating LOC for information systems from their conceptual data models”, in Proceedings of the 28th international conference on Software engineering (ICSE '06), May 20-28, 2006, Shanghai, China, pp. 321-330. DOI: 10.1145/1134285.1134331
7. S. Prykhodko, N. Prykhodko, L. Makarova, and K. Pugachenko, “Detecting Outliers in Multivariate Non-Gaussian Data on the basis of Normalizing Transformations”, in Proceedings of the 2017 IEEE First Ukraine Conference on Electrical and Computer Engineering (UKRCON) «Celebrating 25 Years of IEEE Ukraine Section», May 29 – June 2, 2017, Kyiv, Ukraine, 2017, pp. 846-849. DOI: 10.1109/UKRCON.2017.8100366
8. K. V. Mardia, “Measures of multivariate skewness and kurtosis with applications”, Biometrika, 57, 1970, pp. 519-530. DOI: 10.1093/biomet/57.3.519
Published
2018-11-21
How to Cite
Приходько, С. Б., & Приходько, Н. В. (2018). Constructing the nonlinear regression equations based on multivariate normalizing transformations. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 39(3), 61-68. Retrieved from https://periodicals.karazin.ua/mia/article/view/12817
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