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Nonparametric Statistics, spring 2009


Sangita Kulathinal


6 cu.


Intermediate studies.


Understanding of statistical inference concepts (parameters, estimation and hypothesis testing) and probability.


The course will cover concepts of parametric and nonparametric statistics, hypothesis tests, ranks, order statistics and U-statistics, classical distribution-free tests. The course will also introduce Bayesian nonparametrics. Some practical applications using package R will be considered.

Course content

  • Concepts of parametric and nonparametric statistics
  • Nonparametric Methods: order statistics and their distributions
  • Empirical distribution functions, Kolmogorov-Smirnov test for the equality of two distribution functions
  • Tests and confidence intervals for population quantiles
  • Sign test, test for symmetry, signed-rank test, Wilcoxon-Mann-Whitney test, Kruskal-Wallis test, run test, tests for independence
  • Nonparametric measures of correlations
  • Concepts of asymptotic efficiency
  • Bayesian nonparametrics


Weeks 14-20, three days a week.

(warning) First lecture on Wednesday 1.4.

Mon 10-12 C323
Tue 12-14 C323
Wed 10-12 B120

Easter holiday 9.-15.4.

Course notes

Discussions, home assignments and  exercises

U-statistics (available from

Correlation and Regression without Sum of Squares (Kendall's tau), Rudy A. Gideon (available from

A Bayesian Analysis of Some Nonparametric Problems, Thomas S. Ferguson, The Annals of Statistics, Vol. 1, No. 2. (Mar., 1973), pp. 209-230. (Link:

Nonparametric Bayes estimation of a distribution function with truncated data, Journal of Statistical Planning and Inference
Volume 55, Issue 3, 8 November 1996, Pages 361-369 (Link: doi:10.1016/S0378-3758(95)00195-6) 

Bayesian Nonparametric Inference for Random Distribution and Related Functions. S.G. Walker, P. Damien, P.W. Laud, A.F.M. Smith. Journal of the Royal Statistical Society, Series B (Statistical Methodology), 61(3):485-527, 1999. (Link:

Exercise 1 (8 April, 2009)

Exercise 2 (22 April, 2009)

Exercise 3 (11 May, 2009)

Exercise 4 (12 May, 2009)

Exercise 5 (13 May, 2009)

Course work (to be submitted by 20 May, 2009) 


Home assignments during the course.


Lehmann EL (1975). Nonparametrics: Statistical Methods Based on Ranks.
San Francisco: Holden-Day, Inc.

Sidak Z, Sen PK, and Hajek J (1999). Theory of Rank Tests.
Academic Press; 2 edition.

Gibbons JD (1992). Nonparametric Statistics: An Introduction.
Sage Publications, Inc.

Casella G and Berger RL (2001). Statistical Inference.
Duxbury Press; 2 edition.

Sprent P, Smeeton NC (2001). Applied Nonparametric Statistical methods.  3rd Edition, , Chapman & Hall/CRC.

Ghosh JK and Ramamoorthi RV (2003). Bayesian Nonparametrics. Springer.


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Exercise groups

There will be two hours of exercise classes per week.

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