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1 = Nonparametric Statistics, spring 2009 =
2
3 === Lecturer ===
4
5 [[Sangita Kulathinal>>doc:mathstatHenkilokunta.Kulathinal, Sangita]]
6
7 === Scope ===
8
9 6 cu.
10
11 === Type ===
12
13 Intermediate studies.
14
15 === Prerequisites ===
16
17 Understanding of statistical inference concepts (parameters, estimation and hypothesis testing) and probability.
18
19 === Description ===
20
21 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.
22
23 === Course content ===
24
25 * Concepts of parametric and nonparametric statistics
26 * Nonparametric Methods: order statistics and their distributions
27 * Empirical distribution functions, Kolmogorov-Smirnov test for the equality of two distribution functions
28 * Tests and confidence intervals for population quantiles
29 * Sign test, test for symmetry, signed-rank test, Wilcoxon-Mann-Whitney test, Kruskal-Wallis test, run test, tests for independence
30 * Nonparametric measures of correlations
31 * Concepts of asymptotic efficiency
32 * Bayesian nonparametrics
33
34 === Lectures ===
35
36 Weeks 14-20, three days a week.
37
38 First lecture on Wednesday 1.4.
39
40 Mon 10-12 C323
41 Tue 12-14 C323
42 Wed 10-12 B120
43
44 Easter holiday 9.-15.4.
45
46 [[Course notes>>attach:nonpara-course-notes.pdf]]
47
48 \\
49
50 Discussions, home assignments and  exercises
51
52 U-statistics (available from [[http:~~/~~/www.math.ucla.edu/~~~~tom/Stat200C/Ustat.pdf>>url:http://www.math.ucla.edu/~~tom/Stat200C/Ustat.pdf||shape="rect"]])
53
54 Correlation and Regression without Sum of Squares (Kendall's tau), Rudy A. Gideon (available from [[http:~~/~~/www.math.umt.edu/gideon/Kendelemslp.pdf>>url:http://www.math.umt.edu/gideon/Kendelemslp.pdf||rel="nofollow" shape="rect" class="external-link"]])
55
56 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>>url:http://links.jstor.org/sici?sici=0090-5364%28197303%291%3A2%3C209%3AABAOSN%3E2.0.CO%3B2-U||shape="rect"]])
57
58 Nonparametric Bayes estimation of a distribution function with truncated data, Journal of Statistical Planning and Inference
59 Volume 55, Issue 3, 8 November 1996, Pages 361-369 (Link: doi:10.1016/S0378-3758(95)00195-6)
60
61 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>>url:http://www3.interscience.wiley.com/cgi-bin/fulltext/119099503/PDFSTART||shape="rect"]])
62
63 [[Exercise 1>>attach:p1.pdf]] (8 April, 2009)
64
65 [[Exercise 2>>attach:p2.pdf]] (22 April, 2009)
66
67 [[Exercise 3>>attach:p3.pdf]] (11 May, 2009)
68
69 [[Exercise 4>>attach:p4.pdf]] (12 May, 2009)
70
71 [[Exercise 5>>attach:p5.pdf]] (13 May, 2009)
72
73 [[Course work>>attach:coursework.pdf]] (to be submitted by 20 May, 2009)
74
75 === Exams ===
76
77 Home assignments during the course.
78
79 === Bibliography ===
80
81 Lehmann EL (1975). Nonparametrics: Statistical Methods Based on Ranks.
82 San Francisco: Holden-Day, Inc.
83
84 Sidak Z, Sen PK, and Hajek J (1999). Theory of Rank Tests.
85 Academic Press; 2 edition.
86
87 Gibbons JD (1992). Nonparametric Statistics: An Introduction.
88 Sage Publications, Inc.
89
90 Casella G and Berger RL (2001). Statistical Inference.
91 Duxbury Press; 2 edition.
92
93 Sprent P, Smeeton NC (2001). Applied Nonparametric Statistical methods.  3rd Edition, , Chapman & Hall/CRC.
94
95 Ghosh JK and Ramamoorthi RV (2003). Bayesian Nonparametrics. Springer.\\
96
97 === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57740||shape="rect"]] ===
98
99 Did you forget to register? [[What to do>>doc:mathstatOpiskelu.Kysymys4]].
100
101 === Exercise groups ===
102
103 There will be two hours of exercise classes per week.