Natural Transformations in Statistics

Kondratiev, Gennadii V.

doi:10.18052/www.scipress.com/IFSL.6.1

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Natural Transformations in Statistics

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Abstract:

The old idea of internal uniform regularity of empirical data is discussed within the framework of category theory. A new concept and technique of statistical analysis is being introduced. It is independent on and fully compatible with the classical probabilistic approach. The absence of the model in the natural approach to statistics eliminates the model error and allows to use it in all areas with poor models. The existing error is fully determined by incompleteness of the data. It is always uniformly small by the construction of the data extension.

Info:

Periodical:

International Frontier Science Letters (Volume 6)

Pages:

1-5

DOI:

https://doi.org/10.18052/www.scipress.com/IFSL.6.1

Citation:

G. V. Kondratiev, "Natural Transformations in Statistics", International Frontier Science Letters, Vol. 6, pp. 1-5, 2015

Online since:

December 2015

Authors:

Gennadii V. Kondratiev

Keywords:

Category Theory, Data, Internal Property, Invariants, Natural Extensions, Natural Transformations, Uniform Regularity

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Open Access

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Creative Commons Attribution 4.0 International License

References:

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DOI: https://doi.org/10.1090/s0002-9947-1945-0013131-6

[2] S. Maclane, Categories for the Working Mathematician, second ed., Springer-Verlag, New York, (1998).

[3] F. Klein, Vergleichende Betrachtungen ber geometrische Forschungen, Erlanger Programm. 1872.

[4] E. Cartan, La méthode de repère mobile, la théorie des groupes continus, et les espaces généralisés, Actualités Scientifiques et Industrielles no. 194, (1935).

DOI: https://doi.org/10.1017/s0025557200204531

[5] B. Jacobs, Categorical Logic and Type Theory. Elsevier, North-Holland, (2001).

[6] G. V. Kondratiev, A Categorical-Informational Approach to the Value Prediction Problem, Atti della Accademia Peloritana dei Pericolanti: Classe di Scienze Fisiche, Matematiche e Naturali, Vol. 91, No. 2, A3, 11 p. p., URL: http: /dx. doi. org/10. 1478/AAPP. 912A3, (2013).

DOI: https://doi.org/10.1007/bf02959921

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