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Nonparametric Statistics, spring 2009

Lecturer

Sangita Kulathinal

Scope

6 cu.

Type

Intermediate studies.

Prerequisites

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

Description

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

Lectures

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 http://www.math.ucla.edu/~tom/Stat200C/Ustat.pdf)

Correlation and Regression without Sum of Squares (Kendall's tau), Rudy A. Gideon (available from http://www.math.umt.edu/gideon/Kendelemslp.pdf)

A Bayesian Analysis of Some Nonparametric Problems, Thomas S. Ferguson, The Annals of Statistics, Vol. 1, No. 2. (Mar., 1973), pp. 209-230. (Link: http://links.jstor.org/sici?sici=0090-5364%28197303%291%3A2%3C209%3AABAOSN%3E2.0.CO%3B2-U)

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: http://www3.interscience.wiley.com/cgi-bin/fulltext/119099503/PDFSTART)

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) 

Exams

Home assignments during the course.

Bibliography

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.

Registration

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Exercise groups

There will be two hours of exercise classes per week.

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