Non Parametric Statistics (8 ECTS)

    Course Code: 
    6113
    Semester: 
    8th
    Elective Courses
    Διδάσκων: 

    Academic Scholar

    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.