Non Parametric Statistics (8 ECTS)

Course Code: 
Elective Courses

Non parametric density estimation, histograms, Nadaraya-Watson estimator: balancing bias and variation and choosing bandwidth: plug in and cross-validation methods. Non parametric regression: smoothing techniques. Estimator based on Nadaraya-Watson kernels, asymptotic bias and variance growth, bandwidth choice; local polynomial regression and splines; variance estimation and confidence intervals. Generalized additive models (and regression trees). The Empirical distribution function, empirical sequence. Kolmogorov-Smirnoff and similar tests. Statistics based on functionals of the empirical distribution function. Jacknife and Bootstrap: basic principals, examples, parametric bootstrap, estimating the estimators variance and bootstrap confidence intervals. Non parametric tests based on ranks and the concept of robustness and asymptotic relevant efficiency.

 Recommended Reading

  • Efron and Tibshirani (1998), An Introduction to the Bootstrap. Chapman & Hall.
  • Fan, J. and Gijbels, I. (1996). Local polynomial modelling and its applications. Chapman & Hall.
  • Fox, J. (2000).  Nonparametric Simple Regression: Smoothing Scatterplots. Sage Publications.
  • Hajek, J. (1969). A Course in Nonparametric Statistics. Holden Day.
  • Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Additive Models. Chapman and Hall.
  • Hettmansperger, T. and McKean, J. (2011). Robust nonparametric Statistical Methods. Boca Ration : CRC/Taylor & Francis.
  • Higgins, J.  J. (2004). Introduction to Modern Nonparametric Statistics. Thomson/Brooks/Cole, New York.
  • Hollander, M. and  Wolfe, D. A., (1999). Nonparametric Statistical Method. Wiley.
  • Shao and Tu (1995), The Jackknife an the Bootstrap, Springer.
  • Sidak, Z., Sen, P. K. and Hajek, J. (1999). Theory of Rank Tests. Academic Press.
  • Silverman, B.W.(1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall.
  • Wand, M. P. and Jones, M. C. (1994). Kernel Smoothing. Chapman and Hall.
  • Wasserman, L. (2006). All of Nonparametric Statistics. Springer.
  • Wood, Generalized Additive Models.Chapman and Hall.
  • Ξεκαλάκη , Ε. (2001). Μη παραμετρική στατιστική.