Introduction to Theoretical Statistics II (STA 6327)

Syllabus

 

Instructor Office Hours: Monday, Thursday 11:00 am -12:30 pm (Online office hours, Zoom link will be sent the day before)

 

TA Office Hours: Zeyu Yuwen (zeyu.yuwen@ufl.edu) Tuesday, 12 pm – 2 pm (Online office hours, Zoom link will be sent the day before)

 

Exam schedule:

Exam 1: Tuesday, February 11

Exam 2: Wednesday, March 25

Exam 3: Wednesday, April 22

 

Homework: Homeworks, Practice problems, and solutions will be sent via the class email list

 

 

Running list of topics covered in class

Monday, January 6: General statistical framework, fundamental principle of statistics

Wednesday, January 8: Sufficiency, Factorization theorem

Friday, January 10: Method of moments

Monday, January 13: Maximum likelihood estimation – definition

Wednesday, January 15: Maximum likelihood estimation – examples

Friday, January 17: Maximum likelihood example – linear model (derivation of MLE)

Wednesday, January 22: Maximum likelihood – linear model (derivation of distribution of MLE)

Friday, January 24: Maximum likelihood – linear model (derivation of distribution of MLE)

Monday, January 27: EM algorithm – Normal mixture example

Wednesday, January 29: EM algorithm – General form

Friday, January 31: Invariance of the MLE

Monday, February 3: Convergence of the EM algorithm

Wednesday, February 5: EM algorithm – Probit regression

Friday, February 7: Bayesian statistics – Introduction

Monday, February 10: Bayesian statistics – Examples

Wednesday, February 12: Bayesian statistics – Data Augmentatin (DA) algorithm

Friday, February 14: DA algorithm – Probit regression example

Monday, February 17: DA algorithm – Normal mixture example

Wednesday, February 19: Uniformly Minimum Variance Unbiased Estimation (UMVUE) – Introduction

Friday, February 21: UMVUE – Function of complete, sufficient statistic

Monday, February 24: UMVUE – Conditioning on complete, sufficient statistics

Friday, February 26: UMVUE – Proofs

Monday, March 9: Cramer-Rao inequality

Wednesday, March 11: Cramer-Rao inequality (attainment of lower bound)

Friday, March 13: Hypothesis testing – Introduction

Monday, March 16: Likelihood ratio test

Wednesday, March 18: Likelihood ratio test – further examples

Friday, March 20: Size of a test and choice of cutoff for the rejection region

Monday, March 23: Randomized test functions, Binomial LRT

Friday, March 27: Power function and Most Powerful tests

Monday, March 30: Neyman-Pearson lemma – proof

Wednesday, April 1: Neyman-Pearson lemma – examples

Friday, April 3: Karlin-Rubin theorem, p-value

Monday, April 6: Confidence regions

Wednesday, April 8: Revision of convergence concepts

Friday, April 10: Methods of establishing consistency

Monday, April 13: Consistency of MLE

Wednesday, April 15: Methods of establishing asymptotic normality

Friday, April 17: Asymptotic normality of MLE and Lyapunov CLT