MTH665

Welcome!

Class Schedule: T and Th from 11am to 12pm

Discussions: After class, from 12pm to 12:15pm

Makeup Class Schedule: Sat from 11am to 12pm OR 4pm to 5pm

Online Mode: using Zoom

Lecture Notes (ignore the section/sub-section numbering for the first few notes):

• Preparatory

• 1 and addendum

• 2

• 3

• 4

• 5

• 6

• 7

• 8

Video links:

• 1 - A and B

Supplementary Note - 1 , 2

NO CLASS ON SEPTEMBER 8 (TUESDAY) AND SEPTEMBER 10 (THURSDAY)

• 2 - A

• 3 - A and B and C

Supplementary Note - 1 , 2

• 4 - A and B

Supplementary Note - 1 , 2

• 5 - A and B (extras - 1 and 2)

• 6 - A and B

• 7 - A and B

• 8 - A and B

• 9 - A and B

• 10 - A and B

• 11 - A and B

• 12 - A and B

Supplementary Note - 1

• 13 - A

Supplementary Note - 1

Additional material:

• $\pi$ and Monte Carlo

• $L_p$ spaces

• Convergence in distribution - 1 , 2 ,

• Sequence of functions - 1 , 2 ,

• Uniform continuity - note , video ,

• Using LaTeX for basic mathematical equations

• Convergence in distribution, and continuity theorem - 1 , 2 ,

• CLT - 1 , 2 ,

• Stationarity - Check Chapter 3, a really nice note on time series analysis

• Multivariate normal distribution - 1 , 2 ,

• CLT and Alan Turing

• Berry-Esseen papers -1 , 2 ,

• EVT - 1 and 2

• EDF and Quantiles -1 , 2 ,

• Note on Bahadur's expansion - Check Section 3.3.2

• MLE - 1 , 2 , 3 (Check Theorem 4.2.1) ,

• Goodness of fit (Check Sections 3.1 and 3.1.3)

• Anirban Dasgupta's book (use VPN to login to IITK for access)

• Multinomial distribution - 1 (check p.15 onwards), 2 ,

• Result related to chi-squared distribution - Check Theorem 3

• Consistency of tests

• Contiguous/local alternatives - Check lectures starting in April

• More on contiguity

• U statistics - 1 , 2 (Check lecture notes) ,

• ARE - 1 (Check Chapter 5 onwards) , 2 ,

Evaluation:

• Online discussions on Piazza

• Quiz and EndSem on Gradescope

• Graded homeworks on Gradescope

Grading policy:

50% - Graded Homework

10% - Piazza

20% - Two Short Quizzes

20% - EndSem