Special Mathematics Lecture

Statistics (Spring 2019)

Class dates :
April 17, 24
May 8, 15, 22, 29
June 5, 12, 19, 25 (additional lecture), 26 (special lecture on tree based methods)
July 3, 10, 17

Study sessions / trailer for prospective Japanese students
Monday at 6.30 in room 207 of Science Building A, with Liyang and Chang
Tuesday at 6.30 in room 207 of Science Building A, with Song Ha and Tu Ha

Program :
I) Probability theory: Lec. 1, Lec. 2, App. 2, Lec. 3, App. 3
II) Random sample: Lec. 3, Lec. 4, App. 4
III) Data reduction: Lec. 4, Lec. 5, App. 5
IV) Point estimation: Lec. 5, Lec. 6
V) Hypothesis testing: Lec. 7, App. 7, Lec. 8, App. 8
VI) Interval estimation: Lec. 9
VII) Asymptotic evaluations: Lec. 10, App. 10
VIII) Analysis of variance and regression: Lec. 11, Lec. 12
IX) Regression models: Lec. 12, Lec. 13, App. 13
X) The application of tree-based methods for the analysis of MathSciNet database: : Lec. 14 made by Qiwen Sun

The cumulative notes : here (notes taken by Liyang Zhang), the appendix to the lectures

For the evaluation, you need to submit the solutions of some exercises and/or the proofs of some statements. These submissions can take place at any time during the semester. If you have any question, contact me or Qiwen.

Works submitted by the students :
On Bernoulli distribution, by Keito Masuda
Exercises about median, skewness and kurtosis, by Zhengliang Zhu
On negative binomial distribution, by Tomoya Tatsuno and Thannawat Kanokviboonsri
On student t-distribution, by Yoshihiko Terasawa and Naohiro Tsuzu
On logistic distribution, by Liyang Zhang and Tu Ha Bui
On covariance and linear dependence, by Liyang Zhang
Ex. 2.28 of [CB], by Song Ha, Liyang Zhang, Sun Chang, Tomoya Tatsuno, Takahiro Tabuchi, and Arata Suzuki
Thm. 5.4.4 of [CB], by Tu Ha Bui
Gamma function and gamma distribution, by Sparsh Mishra
Ex. 7.22 of [CB], by Tu Ha Bui and Song Ha
On Cauchy distribution, by Yong Jian Ng and Tho Qing (Jeremy) Pang
Discrete uniform distribution, by Prerna Lavania and Nadia Eliora
On 1-a confidence interval, by Song Ha and Cong Bui
Exercises on Chapter 3 and 7, by Zhengliang Zhu
On asymptotic efficiency: Thm 10.1.12 of [CB], by Tu Ha Bui
On binomial distribution, by Dam Truyen Duc
On Fisher's theorem, by James Boyle
Exercises on Chapter 9 and 11, by Zhengliang Zhu
On 1-a confidence interval, by Sun Chang
On chi^2 distribution, by Sun Chang and Tumul Kumar
Conditional distributions and independence, by Prerna Lavania, Nadia Eliora, and Dam Truyen Duc
On Poisson distribution, by Song Ha and Cong Bui
A few exercises, by Patrick Finke
The exponential distribution, by Patrick Finke and Zhengliang Zhu

References : (electronic version available upon request)
[An] T.W. Anderson, An introduction to multivariate statistical analysis. A reference book, but a little bit old
[BD_I] and [BD_II] P.J. Bickel, K.A. Doksum, Mathematical statistics: basic ideas and selected topics. Extended version of a classical book of 1977
[CB] G. Casella, R.L. Berger, Statistical inference. Our main reference, seems very good
[CBS] G. Casella, R.L. Berger, D. Santana, Solutions for Statistical inference. Very helpful
[FEHP] C. Forbes, M. Evans, N. Hastings, B. Peacock, Statistical distributions. Useful information on many common distributions
[GW] G. Grimmett, D. Welsh, Probability: an introduction. Contains all you need to know about probability
[Ke] R.W. Keener, Theoretical Statistics: topics for a Core Course. Slightly more advanced
[LC] E.L. Lehmann, G. Casella, Theory of point estimation. For further reading, a classic
[LR] E.L. Lehmann J.P. Romano, Testing Statistical Hypotheses. For further reading, another classic
[Ri] J.A. Rice, Mathematical statistics and data analysis.
[vdG] S. van de Geer, Mathematical statistics. Lecture notes used in ETH, Zurich
[Wa] L. Wasserman, All of statistics: a concise course in statistical inference. Contains a lot