Goodness of Fit

  • Anirban DasGupta
Part of the Springer Texts in Statistics book series (STS)


Empirical Process Brownian Bridge Asymptotic Null Distribution Density Power Divergence Empirical Process Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, T.W. (1962). On the distribution of the two sample Cramér-von Mises criterion, Ann. Math. Stat., 33, 1148–1159.CrossRefGoogle Scholar
  2. Araujo, A. and Giné, E. (1980). The Central Limit Theorem for Real and Banach Valued Random Variables, Wiley, New York.zbMATHGoogle Scholar
  3. Basu, A., Harris, I., Hjort, N., and Jones, M. (1998). Robust and efficient estimation by minimizing density power divergence, Biometrika, 85, 549–559.zbMATHCrossRefMathSciNetGoogle Scholar
  4. Berk, R. and Jones, D. (1979). Goodness of fit statistics that dominate the Kolmogorov statistics, Z. Wahr. Verw. Geb., 47, 47–59.zbMATHCrossRefMathSciNetGoogle Scholar
  5. Bickel, P.J. (1968). A distribution free version of the Smirnov two sample test in the p-variate case, Ann. Math. Stat., 40, 1–23.CrossRefMathSciNetGoogle Scholar
  6. Billingsley, P. (1999). Convergence of Probability Measures, 2nd ed., John Wiley, New York.zbMATHGoogle Scholar
  7. Brown, L., DasGupta, A., Marden, J., and Politis, D.(2004). Characterizations, Sub and Resampling, and Goodness of Fit, IMS Lecture Notes Monograph Series, Vol. 45, Institute of Mathematical Statistics, Beachwood, OH, 180–206.Google Scholar
  8. Csizár, I. (1963). Magy. Tud. Akad. Mat. Kutató Int. Közl, 8, 85–108 (in German).Google Scholar
  9. Csörgo, M., Csörgo, S., Horváth, L., and Mason, D. (1986). Weighted empirical and quantile process, Ann. Prob., 14, 31–85.CrossRefGoogle Scholar
  10. D’Agostino, R. and Stephens, M. (1986). Goodness of Fit Techniques, Marcel Dekker, New York.Google Scholar
  11. de Wet, T. and Ventner, J. (1972). Asymptotic distributions of certain test criteria of normality, S. Afr. Stat. J., 6, 135–149.Google Scholar
  12. del Barrio, E., Deheuvels, P., and van de Geer, S. (2007). Lectures on Empirical Processes, European Mathematical Society, Zurich.zbMATHGoogle Scholar
  13. Gnanadesikan, R. (1997). Methods for Statistical Data Analysis of Multivariate Observations, John Wiley, New York.Google Scholar
  14. Groeneboom, P. and Shorack, G. (1981). Large deviations of goodness of fit statistics and linear combinations of order statistics, Ann. Prob., 9, 971–987.zbMATHCrossRefMathSciNetGoogle Scholar
  15. Hodges, J.L. (1958). The significance probability of the Smirnov two sample test, Ark. Mat., 3, 469–486.zbMATHCrossRefMathSciNetGoogle Scholar
  16. Jager, L. (2006). Goodness of fit tests based on phi-divergences, Technical Report, University of Washington.Google Scholar
  17. Jager, L. and Wellner, J. (2006). Goodness of fit tests via phi-divergences, in Press.Google Scholar
  18. Kiefer, J. (1959). k sample analogues of the Kolmogorov-Smirnov and the Cramér-von Mises tests, Ann. Math. Stat., 30, 420–447.CrossRefMathSciNetGoogle Scholar
  19. Kolmogorov, A. (1933). Sulla determinazione empirica di una legge di distribuzione, Giorn. Ist. Ital. Attuari, 4, 83–91.Google Scholar
  20. Lehmann, E.L. (1999). Elements of Large Sample Theory, Springer, New York.zbMATHGoogle Scholar
  21. Marden, J. (1998). Bivariate qq and spider-web plots, Stat. Sinica, 8(3), 813–816.zbMATHMathSciNetGoogle Scholar
  22. Marden, J. (2004). Positions and QQ plots, Stat. Sci., 19(4), 606–614.zbMATHCrossRefMathSciNetGoogle Scholar
  23. Martynov, G.V. (1992). Statistical tests based on Empirical processes and related problems, Sov. J. Math., 61(4), 2195–2271.CrossRefMathSciNetGoogle Scholar
  24. Owen, A. (1995). Nonparametric likelihood confidence hands for a distribution function, J. Amer. Stat., Assoc., 90, 430, 516–521.zbMATHCrossRefMathSciNetGoogle Scholar
  25. Pollard, D. (1989). Asymptotics via Empirical processes, Stat. Sci., 4(4), 341–366.zbMATHCrossRefMathSciNetGoogle Scholar
  26. Raghavachari, M. (1973). Limiting distributions of the Kolmogorov-Smirnov type statistics under the alternative, Ann. Stat., 1, 67–73.zbMATHCrossRefMathSciNetGoogle Scholar
  27. Sarkadi, K. (1985). On the asymptotic behavior of the Shapiro-Wilk test, in Proceedings of the 7th Conference on Probability Theory, Brasov, Romania, IVNU Science Press, Utrecht, 325–331.Google Scholar
  28. Shapiro, S.S. and Wilk, M.B. (1965). An analysis of variance test for normality, Biometrika, 52, 591–611.zbMATHMathSciNetGoogle Scholar
  29. Shorack, G. and Wellner, J. (1986). Empirical Processes, with Applications to Statistics, John Wiley, New York.Google Scholar
  30. Smirnov, N. (1941). Approximate laws of distribution of random variables from empirical data, Usp. Mat. Nauk., 10, 179–206 (in Russian).Google Scholar
  31. Stephens, M. (1993). Aspects of Goodness of Fit:Statistical Sciences and Data Analysis, VSP, Utrecht.Google Scholar
  32. Stuart, A. and Ord, K. (1991). Kendall’s Advanced Theory of Statistics, Vol. II, Clarendon Press, New York.Google Scholar
  33. Wald, A. and Wolfowitz, J. (1940). On a test whether two samples are from the same population, Ann. Math. Stat., 11, 147–162.CrossRefMathSciNetGoogle Scholar
  34. Wald, A. and Wolfowitz, J. (1941). Note on confidence limits for continuous distribution functions, Ann. Math. Stat., 12, 118–119.CrossRefMathSciNetGoogle Scholar
  35. Weiss, L. (1960). Two sample tests for multivariate distributions, Ann. Math. Stat., 31, 159–164.CrossRefGoogle Scholar
  36. Wellner, J. and Koltchinskii, V. (2003). A note on the asymptotic distribution of the Berk-Jones type statistics under the null distribution, in High Dimensional Probability III, Progress in Probability, J. Hoffman Jørgensen, M. Marcus and J. Wellner (eds.), Vol. 55, Birkhäuser, Basel, 321–332.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Anirban DasGupta
    • 1
  1. 1.Department of StatisticsPurdue UniversityWest Lafayette

Personalised recommendations