Nonparametric Approaches for e-Learning Data

  • Paolo Baldini
  • Silvia Figini
  • Paolo Giudici
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4065)


In the paper we propose nonparametric approaches for e-learning data. In particular we want to supply a measure of the relative exercises importance, to estimate the acquired Knowledge for each student and finally to personalize the e-learning platform. The methodology employed is based on a comparison between nonparametric statistics for kernel density classification and parametric models such as generalized linear models and generalized additive models.


Kernel Function Generalize Additive Model Smoothing Parameter Kernel Density Estimation Nonparametric Approach 
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. 1.
    Azzalini, A., Bowman, A.W.: Applied Smoothing Techniques for Data Analysis. Oxford Statistical Science Series. Oxford (1997)Google Scholar
  2. 2.
    Fan, J., Gijbels, I.: Local Polynomial Modelling and Ist Applications. Chapman Hall, London (1996)Google Scholar
  3. 3.
    Giudici, P.: Applied data mining. Wiley, Chichester (2003)MATHGoogle Scholar
  4. 4.
    Green, P.J., Silverman, B.W.: Nonparametric Regression and Generalized Linear Models: A Roughness Penality Approach. Chapman Hall, London (1994)Google Scholar
  5. 5.
    Hastie, T.J., Tibshirani, R.J.: Generalized Additive Models. Chapman Hall, London (1990)MATHGoogle Scholar
  6. 6.
    Scott, D.W.: Multivariate Density Estimation: Theory, Practice and Visualisation. Wiley, New York (1992)CrossRefGoogle Scholar
  7. 7.
    Simonoff, J.S.: Smoothing Methods in Statistics. Springer, New York (1996)MATHGoogle Scholar
  8. 8.
    Wand, M.P., Jones, M.C.: Kernel Smoothing. Chapman Hall, London (1995)MATHGoogle Scholar
  9. 9.
    Bjerve, S., Doksum, K.: Correlation curves measures of association as functions of covariate values. Ann. Statist. 21, 890–902 (1993)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Bowman, A.W.: An alternative method of cross validation for the smoothing of density estimates. Biometrika 711, 353–360 (1984)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Bowman, A.W., Foster, P.J.: Adaptive smoothing and density based tests of multivariate normality. J. Amer. Statist. Assoc. 88, 529–573 (1993)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Doksum, K., Blyth, S., Bradlow, E., Meng, X.L., Zhao, H.: Correlation curves as local measures of variance explained by regression. J. Amer. Statist. Assoc. 89, 571–582 (1994)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Jones, M.C., Marron, J.S., Sheather, S.J.: A brief survey of bandwidth selection for density estimation. J. Amer. Statist. Assoc. 91, 401–407 (1996)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Parzen, E.: On the estimation of a probability density and mode. Ann. Math. Statist. 33, 1065–1076 (1962)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Rosenblatt, M.: Remarks on some noparametric estimates of a density function. Ann. Meth. Statist. 27, 832–837 (1956)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Rudemo, M.: Empirical choice of histograms and kernel density estimators. Scand. J. Statist. 9, 65–78 (1982)MATHMathSciNetGoogle Scholar
  17. 17.
    Scott, D.W., Terrell, G.: Biased and unbiased cross validation in density estimation. J. Amer. Statist. Assoc. 82, 1131–1146 (1987)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Sheather, S.J., Jones, M.C.: A reliable data based bandwidth selection method for kernel density estimation. J. Roy. Statist. Soc. Ser. B 53, 683–690 (1991)MATHMathSciNetGoogle Scholar
  19. 19.
    Stone, M.A.: Cross validatory choice and assessment of statistical predictions. J. Roy. Statist. Soc. Ser. B 36, 111–147 (1974)MATHMathSciNetGoogle Scholar
  20. 20.
    Taylor, C.C.: Boostrap choice of the smoothing parameter in kernel density estimation. Biometrika 36, 111–147 (1989)Google Scholar
  21. 21.
    Whittle, P.: On the smoothing of probability density functions. J. Roy. Statist. Soc. Ser. B 55, 549–557 (1958)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Paolo Baldini
    • 1
  • Silvia Figini
    • 1
  • Paolo Giudici
    • 1
  1. 1.University of PaviaPaviaItaly

Personalised recommendations