/ W&I / Mathematics / 2WS00
 Mathematical Statistics (2WS05)

This course is the successor of the course 2S990.

Lecturer: A. Di Bucchianico, HG 10.17, phone +31 (0)40 247 2902, email:

Instructor: S. Kuhnt, HG 10.23, phone +31 (0)40 247 2208, email:

Prerequisites: in order to successfully participate in this course, it is essential to have passed the examination for the course 2S270: Probability theory and statistics.

Software: R, to be obtained from www.r-project.org, and Statgraphics (to be obtained from the TU/e software website) . I wrote an introduction to R which includes some exercises. There is a PowerPoint presentation for a very quick introduction to R .

## Material:

• Lecture notes Measures of Location and Scale
• Bain and Engelhardt, Introduction to probability and mathematical statistics, Brooks/Cole, 2000.
• Statistisch Compendium (lecture notes nr. 2218)

## Data sets

In lecture notes (LN): copper (Example 1.1), suicide ( Example 1.2) , darwin (Example 1.3) and mercury (Example 1.13)

In Section 1.3 of Introduction to R (IR): eggs, supermarket, telephone, light, and clouds.

In Bain and Engelhardt (BE): example 4.6.3 = example 11.1.1, exercise 4.24 = exercise 11.2

## Schedule

 Week Topic Sections in lecture (LN). Introduction to R (IR), or book (BE) Recommended exercises (new 2007-2008 numbering!) 1 Statistical software, measures of location and dispersion, boxplots LN 1.1-1.3, IR 1.1-1.2 , LN 1.12, IR 5, 6, 7, LN 1.9, 1.14; solutions: IR 5, 6, 7 2 Empirical distributions and equivariance LN 1.4-1.5 IR 8; LN 1.15, 1.17, 1.18, 1.6 solution: IR 8 3 Outliers; Point estimation: construction (MME and ML) LN 1.6.1-1.6.2; BE 9.1-9.2 LN 1.22, 1.26, 1.28 ; BE 9.1, 9.4, 9.5, 9.8: examination Nov. 2005: 4a, Jan. 2006: 4b 4 Point estimation: M-estimators, performance LN 1.7.1-1.7.2, BE 8.1, 8.2, 9.3, 9.4 only pp. 316-318 BE 9.17, 9.22, 9.24, 9.33, 9.34 a-f, 9.40, LN 1.41, 1.45, 1.46, examination Nov. 2003: 3, Nov. 2005: 4c, Jan. 2006: 2 5 no teaching 6 Sufficiency and completeness BE 10.1 - 10.3, 10.4 only definition of completeness + Lehmann-Scheffé BE 10.1, 10.2, 10.10, 10.21, 10.31, examination Nov. 2002: 1 a-b, Nov. 2003: 1, Jan. 2004: 2, Nov. 2005: 4b, Jan. 2006: 4a 7 Sampling distributions BE 8.3 - 8.5 (use both statistical tables and R): IR 1, 2, 3; BE 8.1, 8.5, 8.8, 8.10, 8.11, 8.16, 8.17 a+b; examination Nov. 2002: 3b, Jan. 2006: 3a + 4c 8 Interval estimation (small R script to compute confidence intervals) BE 11.1 - 11.3,11.5 (use both statistical tables and R): BE 11.1, 11.2, 11.4, 11.12, 11.20, 11.29 a-b, IR: 9, examination Nov. 2003: 5, Jan. 2004: 4c, Nov. 2005: 4b, Jan. 2006: 1c, 3b 9 Hypothesis testing BE 12.1 - 12.5; BE 12.1, 12.3, 12.5, 12.8, 12.9, IR: 11, 12, examination Nov. 2001: 2 a+b, Nov. 2002: 5, Jan. 2003: 5, Nov. 2005: 1 , Jan. 2006: 1 10 Hypothesis testing BE 12.6 - 12.8 BE 12.16, 12.17, 12.27, examination Jan. 2003: 4 , Nov. 2005: 5 , Jan. 2006: 5

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