Math 12640: Advanced Theory of Statistics
Course Description
This is a core course in statistical theory for first or second year graduate students in statistics, probability, or related fields.
Prerequisites: A good knowledge of advanced calulus and linear algebra; previous exposure to probability and mathematical statistics at the undergraduate level;
a course in measure-theoretic probability is recommended but can be taken at the same time.
Syllabus (updated 12/17)
Announcements
Midterm exam: Saturday, November 15, 8:00–10:00 am, 420 Teaching Building 2
Midterm exam solutions and reading materials posted on Teaching and Learning@PKU
Final exam: Thursday, January 8, 2:00–4:00 pm, 204 Teaching Building 3
Office hours in the final week: Tuesday, January 6, 2:00–4:00 pm, 28 Quanzhai
Weekly Topics
Week 1: Shao 1.1–1.3.1
Week 2: Shao 1.3.2–1.4.3 (Mon), 1.5.1–1.5.2 (Wed)
Week 3: Shao 1.5.3–1.5.5
Week 4: No class (Mon), Shao 2.1–2.2.2 (Wed)
Week 5: Shao 2.2.2–2.3.2
Week 6: No class (Mon), Shao 2.3.2–2.4.2 (Wed)
Week 7: Shao 2.4.2–2.5.1 (Mon), 2.5.2–2.5.3 (Wed)
Week 8: Shao 3.1.1–3.1.3 (Mon), 3.1.3–3.1.4 & 3.5.2 (Wed)
Week 9: Midterm exam
Week 10: Shao 4.1.1 & 4.1.3 (Mon), 4.2.1–4.2.2 & 4.3.1 (Wed)
Week 11: Shao 4.4.1–4.4.2
Week 12: Shao 4.4.2 & 4.5.1 (Mon), 4.5.2 & 6.1.1 (Wed)
Week 13: Shao 6.1.2–6.2.1
Week 14: Shao 6.2.2 & 6.4.1–6.4.2 (Mon), 6.4.2–6.4.3 (Wed)
Week 15: Shao 6.4.4, van der Vaart 18.2 & 19.1–19.2
Week 16: van der Vaart 19.2 (Mon), 19.4 & 5.3 (Wed)
Homework Assignments
HW1 (due 9/29)
Shao Chapter 1: 9, 15, 26, 30, 37, 41, 43, 46, 59, 65, 67, 80, 82, 98, 127, 138
HW2 (due 10/13)
Shao Chapter 1: 144, 146, 152, 154, 161, 166; Chapter 2: 9, 11, 22
HW3 (due 10/27)
Shao Chapter 2: 45, 52, 56, 61, 63, 74, 80, 84, 92
HW4 (due 11/15)
Shao Chapter 2: 105, 111, 117, 121, 124; Chapter 3: 2, 5, 24, 40, 110
HW5 (due 12/1)
Shao Chapter 4: 3, 7, 12, 35, 48, 72, 77, 94, 100, 104
HW6 (due 12/15)
Shao Chapter 4: 111, 125, 132; Chapter 6: 3, 6, 15, 22, 28
HW7 (due 12/29)
Shao Chapter 6: 38, 41, 47, 86, 96, 97, 100, 106
Suggested problems (do not turn in)
van der Vaart Chapter 19: 5, 6, 10
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