Have a personal or library account? Click to login
Considering distance measures in Statistics Cover

Considering distance measures in Statistics

Open Access
|Jun 2022

References

  1. Bhattacharyya A. (1943): On a measure of divergence between two statistical populations defined by their probability distributions, Bull. Calcutta Math. Soc. 35, 99–110.
  2. Blyth R.C. (1970): On the Inference and Decision Models of Statistics. The Annals of Mathematical Statistics 41(3), 1034–1058.10.1214/aoms/1177696980
  3. Comber A., Chi K., Huy Q.M., Nguyen Q., Lu B., Phe H.H., Harris P. (2020): Distance metric choice can both reduce and induce collinearity in geographically weighted regression, Environ. Plan. B Urban Anal. City Sci, 47, 489–507.10.1177/2399808318784017
  4. Cover T.M., Thomas J.A. (1991): Elements of Information Theory, Wiley, New York.10.1002/0471200611
  5. Darling D.A. (1957): The Kolmogorov - Smirnov, Gramer - Von Miss tests, Ann Math Stat. 28, 283–838.10.1214/aoms/1177706788
  6. Fisher R.A. (1922): On the mathematical foundation of theoretical statistics, Phil. Trans. Roy. Soc. London, series A 22, 165–177.
  7. Geoghegan D.B. (2008): The Histographic conceptualization of information: A Critical Survey, IEEE Ann. Of History of Computing 30, 66–81.10.1109/MAHC.2008.9
  8. Iliopoulou P., Kitsos C. (2019): Statistical applications in Geography: Spatial Analysis, in Contemporary Essays in Social Sciences & Geography: Theory and Policies, Korres, G., Kourliouros, E., and Kokkinou, A. eds., University of the Aegean, 212–224 (in Greek).
  9. Kamps U. (1989): Hellinger distance and α-entropy in one parameter class of density functions, Stat. Papers, 30, 263–269.10.1007/BF02924332
  10. Kitsos C., Iliopoulou P. (2021): Distance measures in spatial statistics, in Social Sciences & Geography: Theory, Methods and Spatial Analysis techniques, Kalabokidis, K., Korres, G., Soulakellis, N., and Feidas, H. eds. University of the Aegean, 96–108 (in Greek).
  11. Kitsos C., Iliopoulou P. (2022): Adopting Information Distance Measures for Geographical Data Analysis. J. of Regional and Socio-Economic Issues, Vol 12(1), 6–27.
  12. Kitsos C., Toulias L.T. (2010): New information measures for the generalized normal distribution, Information 1, 13–27.10.3390/info1010013
  13. Kitsos C., Toulias L.T. (2017): Hellinger distance between generalized normal distributions, British Journal of Mathematics and Computer Science 21, 1–16.10.9734/BJMCS/2017/32229
  14. Kitsos C., Tavoularis K.N. (2009): Logarithmic Sobolev inequalities for information measures, IEEE Transactions on Information Theory 55 (2009), 2554–2561.10.1109/TIT.2009.2018179
  15. Kitsos C., Sotiropoulos M. (2009). Distance methods for bioassays, Biometrie und Medizinische Informatik Greifswalder Seminarberichte 15, 55–74.
  16. Kolmogorov A. (1933): Sulla determinazione empirica di una legge di distribuzione, G. Ist. Ital. Attuari 4, 83–91.
  17. Kullback S., Leibler A.R. (1951): On Information and sufficiency, Ann. Math. Statist. 22 (1951), 79–86.10.1214/aoms/1177729694
  18. Lu B., Charlton M., Harris P., Fotheringham A.S. (2014): Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data, Int J Geogr. Inf. Sci. 28, 660–681.10.1080/13658816.2013.865739
  19. Mahalanobis C.P. (1936): On the generalized distance in Statistics, Proc. Nat. Inst. of Sciences of India, 2.
  20. Nielsen F. (2011): Chernoff information of exponential families. IEEE Signal Processing Letters 20.3, 269 – 27210.1109/LSP.2013.2243726
  21. Saville J.D., Wood R.G. (1991): Statistical Methods : The Geometric Approach. Springer-Verlag.10.1007/978-1-4612-0971-3
  22. Schervish J.M. (1995): Theory of Statistics, Springer.10.1007/978-1-4612-4250-5
  23. Shanon C.E. (1948): A mathematical theory of communication, Bell Syst. Tech. J. 27, 379–423, 623–656.10.1002/j.1538-7305.1948.tb00917.x
  24. Shapiro S.S., Wilks M.B. (1965): An analysis of variance test for normality (complete samples), Biometrika 65, 591–611.10.1093/biomet/52.3-4.591
  25. Smirnov N. (1948): Table for estimating the goodness of fit of empirical distributions, Annals of Math. Stat. 19, 279–281.10.1214/aoms/1177730256
  26. Takasi S., Takashi S. (2011): Applied Analysis: Mathematical Methods in Natural Science, 2d Edition, Imperial College Press.
  27. Wilson R., Martinez T. (1997): Improved heterogeneous distance functions, J. of Artif. Intell. Res. 6, 1–37.10.1613/jair.346
  28. Wolfowitz J. (1957): The minimum distance method, Ann. Math. Stat 28, 75–87.10.1214/aoms/1177707038
DOI: https://doi.org/10.2478/bile-2022-0006 | Journal eISSN: 2199-577X | Journal ISSN: 1896-3811
Language: English
Page range: 65 - 75
Published on: Jun 30, 2022
Published by: Polish Biometric Society
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2022 Christos P. Kitsos, Constantinos-Symeon Nisiotis, published by Polish Biometric Society
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.