

Cosmological distances scale. Pt. 12. Confluence analysis, rang inversion and tests for inadequacy
https://doi.org/10.32446/0368-1025it.2020-12-13-21
Abstract
The measurement problem of calibration of the cosmological distance scale is considered from the point of view of the conditions of applicability of the regression analysis. It is shown that the rank inversion and statistical heterogeneity of data on supernovae SN ia, which were used in 1998–1999 to detect the “acceleration of the expansion of the Universe”, and in 2004–2007 – as “extraordinary evidence” of its existence, is the reason for the discrepancy and inconsistency of the obtained estimates of the parameters of the Friedman-Robertson-Walker model. Although the use of tests for inadequacy for models of the cosmological distance scale reduces these negative effects, the fact remains that the cosmological distance scale based on redshift has neither the status of metric nor ordinal.
About the Author
S. F. LevinRussian Federation
Sergey F. Levin
Moscow
References
1. Hudson D. J., Statistics: Lectures on Elementary Statistics and Probability, CERN Report 63–29, Geneva, CERN, 1964.
2. Hubble E., Proceedings NAS, 1929, vol. 15, рр. 168–173.
3. Riess A. G. et al., Astronomical Journal, 1998, vol. 116, рр. 1009–1038.
4. Freedman W. L., https://arXiv.org/abs/1706.02739(13Jul2017).
5. Riess Adam G. et al., Preprint Astrophysical Journal, https://arXiv.org/abs/1604.01424v3[astro-ph.CO](9Jun2016).
6. Planck Collaboration: Aghanim N. et al., Astronomy & Astrophysics, 2016, vol. 594, A11.
7. Levin S. F., Measurement Techniques, 2018, vol. 61, no. 11, рр. 1057–1065. https://doi.org/10.1007/s11018-019-01549-6
8. Visser M., https://arXiv.org/abs/gr-qc/0309109v4(31Mar2004).
9. Riess A. et al., https://arXiv.org/abs/1903.07603v2[astroph.CO](27 Mar 2019).
10. Levin S. F., Kontrol’no-izmeritel’ny’e pribory i sistemy, 2006, no. 3, pp. 23–24 (in Russian).
11. Levin S. F., Kontrol’no-izmeritel’ny’e pribory i sistemy, 2006, no. 4, pp. 32–36 (in Russian).
12. Levin S. F., Kontrol’no-izmeritel’ny’e pribory i sistemy, 2006, no. 5, pp. 33–34 (in Russian).
13. Frisch R., Statistical Confl uence Analysis by Means of Complete Regression Systems, Oslo, 1934.
14. Kendall M. A., Stuart A., Inference and Relationship, vol. 2, 2 ed., London, Charles Griffi n & Company Limited, 1963.
15. Ajvazyan S. A., Enyukov I. S., Meshalkin L. D., Prikladnaya statistika: Issledovanie zavisimostej. Spravochnoe izdanie, ed. S. A. Ajvazyan, Moscow, Finansy i statistika Publ., 1985 , 487 p. (in Russian).
16. Vuchkov I., Boyadzhieva L., Solakov E., Prikladnoj linejny`j regressionny`j analiz, Moscow, Finansy i statistika Publ., 1987, 239 p. (in Russian).
17. Greshilov A. A., Analiz i sintez stoxasticheskix sistem. Parametricheskie modeli i konfl yue`ntny`j analiz, Moscow, Radio i svyaz’ Publ., 1990, 320 p. (in Russian).
18. Perlmutter S. et al., Astr ophysical Journal, 1999, vol. 517, рр. 565–586.
19. Riess A. G. et al., Astrophysical Journal, 2004, vol. 607, рр. 665–687.
20. Riess A. G. et al., Astrophysical Journal, 2007, vol. 659, рр. 98–121.
21. Kolmogorov A. N., Lecture Notes in Mathematics no. 1021, Zurich, Springer Science + Business Media books, 1983, pp. 1–5.
22. Draper N. R., Smith H., Applied Regression Analysis, 3 ed., N.Y., Chichester, Weinheim, Brisbane, Singapore, Toronto, John Wiley & Sons, JNC, 1998, 736 p.
23. Freedman W. L., Madore B. F., Gibson B. K., et al., Astrophysical Journal, 2001, V. 553. pp. 47–72.
24. Levin S. F., Measurement Techniques, 2019, vol. 62, no. 1, рр. 7–15. https://doi.org/10.1007/s11018-020-01705-3
25. Mulvey J. H., Statistical methods for processing experimental data, in: High Energy and Nuclear Physics Data Handbook, ed. W. Galbraith, W. S. C. Williams, Chilton, 1963.
26. Hinshaw G. et al., Astrophysical Journal Supplements, 2009, vol. 180, рр. 225–245.
27. Planck Collaboration, Astronomy & Astrophysics, Manuscript Planck Mission 2013, https://arXiv.org/abs/1303.5062v1[astro-ph.CO](20.03.2013).
28. Planck Collaboration, Astronomy & Astrophysics, Manuscript Planck Mission 2015, https://arXiv.org/abs/1502.01589v2[astro-ph.CO](06.02.2015).
29. Levin S. F., Measurement Techniques, 2014, vol. 57, no. 9, рр. 960–966. https://doi.org/10.1007/s11018-014-0566-1
30. Riess A., My Path to the Accelerating Universe, Nobel Lecture, Stockholm, 08 December 2011.
31. Freedman W. L., Madore B. F., Scowcroft V. et al., Astrophysical Journal, 2016, vol. 758, 24 p.
32. Semenov L. A., Siraya T. N., Metody postroeniya graduirovochny’h kharakteristik sredstv izmerenij, Moscow, Izdatel’stvo standartov Publ., 1986, 138 p. (in Russian).
33. Demidenko E. Z., Optimizaciya i regressiya, Moscow, Nauka Publ., 1989, 296 p. (in Russian).
34. Levin S. F., Yadernaya fi zika i inzhiniring, 2014, vol. 5, no. 9–10, pp. 813–818 (in Russian).
35. Levin S. F., Osnovy` teorii kontrolya, Moscow, MO SSSR Publ., 1983, 51 p. (in Russian).
36. Levin S. F., Blinov A. P., Measurement Techniques, 1988, vol. 31, no. 12, рр. 1145–1150. https://doi.org/10.1007/BF00862607
37. Feller W., An Introduction to Probability theory and its Applications, vol. II, 2 ed., N.Y., London, Sydney, Toronto, John Wiley & Sons, Jnc., 1971, 683 p.
38. Levin S. F., Measurement Techniques, 2020, vol. 62, no. 10, pp. 855–862. https://doi.org/10.1007/s11018-020-01705-3
39. Pruzhinskaya M. V., Candidate’s dissertation Mathematics and Physics (MGU, Moscow, 2014).
40. Heckmann O.-H. L., Theorien der Kosmologie, Berlin, Heidelberg, Springer-Verlag, 1942.
41. Levin S. F., Lisenkov A. N., Sen‘ko O. V., Harat‘yan E. I., Sistema metrologicheskogo soprovozhdeniya staticheskih izmeritel`ny`h zadach “MMK-stat M”. Rukovodstvo pol`zovatelya, Moscow, Gosstandart RF, VCz RAN Publ., 1998 (in Russian).
42. Levin S. F., Measurement Techniques, 2016, vol. 59, no. 8, pp. 791–802. https://doi.org/10.1007/s11018-016-1047-5
43. Levin S. F., Optimal`naya interpolyacionnaya fi l`traciya Nstatisticheskih harakteristik sluchajny`h funkcij v determinirovannoj versii metoda Monte-Karlo i zakon krasnogo smeshheniya, Moscow, AN SSSR Publ., 1980, 56 p. (in Russian).
Review
For citations:
Levin S.F. Cosmological distances scale. Pt. 12. Confluence analysis, rang inversion and tests for inadequacy. Izmeritel`naya Tekhnika. 2020;(12):13-21. (In Russ.) https://doi.org/10.32446/0368-1025it.2020-12-13-21