Spring 2019 Course Syllabus:  Math 665

 

Course Title:

Statistical Inference

Textbook:

Introduction to Mathematical Statistics,  by Hogg, McKean, and Craig; Publisher: Pearson, 7th edition (2013); ISBN: 978-0321795434.

 

Prerequisites:

Math 662 or departmental approval.

 

 

Course Outline

Date

Lecture

Sections

Topic

Assignment

Week 1

1/22

1

 

 

Chapter 5

 

CONSISTENCY AND LIMITING DISTRIBUTIONS
Convergence; central limit theorem; delta method; moment generating functions

 

Week 2

1/29

2

Chapter 4

SOME ELEMENTARY STATISTICAL INFERENCE
Sampling and statistics; confidence intervals; hypothesis testing

Homework 1

Week 3

2/5

3

Chapter 6

 

MAXIMUM LIKELIHOOD METHODS
Rao-Cramer lower bound and efficiency; plug-in estimators; method of moments

 

Week 4

2/12

4

Chapter 6

MAXIMUM LIKELIHOOD METHODS (CONTINUED)
Maximum likelihood tests; multiparameter case: estimation and testing

Homework 2

Week 5

2/19

5

Chapter 7

SUFFICIENCY
Sufficient statistic and properties: Rao Blackwell; completeness and uniqueness

  

Week 6

2/26

6

Chapter 7

SUFFICIENCY (CONTINUED)
Minimum variance unbiased estimators; exponential family; functions of a parameter

Homework 3

Week 7

3/5

 

 

MIDTERM EXAM:

Tuesday ~ March 5, 2019

 

Week 8

3/12

7

Chapter 7

SUFFICIENCY (CONTINUED)
Minimal sufficiency; ancillary statistics; sufficiency, completeness and independence

 

Week 9

3/19

 

 

SPRING RECESS (NO CLASSES)

 

 

Week 10

3/26

8

Chapter 8

OPTIMAL TESTS OF HYPOTHESES
Most powerful tests; Neyman-Pearson lemma

Homework 4

 

Week 11

4/2

9

Chapter 8

OPTIMAL TESTS OF HYPOTHESES (CONTINUED)
Uniformly most powerful tests; likelihood ratio tests; monotone likelihood ratio

 

Week 12

4/9

10

Chapter 8

OPTIMAL TESTS OF HYPOTHESES (CONTINUED)
The sequential probability ratio test

 Homework 5

Week 13

4/16

11

Chapter 9

INFERENCE ABOUT NORMAL MODELS
Quadratic forms; ANOVA     

 

Week 14

4/23

12

Chapter 9

INFERENCE ABOUT NORMAL MODELS (CONTINUED)
Multiple comparisons; tests for independence; linear regression

 Homework 6

Week 15

4/30

13

 

REVIEW FOR FINAL EXAM

 

Week 16

5/7

 

 

NO CLASS ~ Follow a Friday Schedule

 

Week 17

5/14

 

 

FINAL EXAM:

Tuesday ~ May 14, 2019

 

 

 

IMPORTANT DATES

FIRST DAY OF SEMESTER

January 22, 2019

LAST DAY TO WITHDRAW

April 8, 2019

LAST DAY OF CLASSES

May 7, 2019

FINAL EXAM PERIOD

May 10 – 16, 2019

 

Grading Policy

 

Assignment Weighting

 

Tentative Grading Scale

Homework

25 %

 

A

90 -- 100

Midterm Exam

35 %

 

B+

80 -- 89

Final Exam

40 %

 

B

75 -- 79

 

 

 

C+

70 -- 74
     

C

60 -- 69

 

 

 

F

0 -- 59

 

 

 

Important Departmental and University Policies

 

Prepared by Prof. Wenge Guo, January 10, 2019