STAT 5010

Advanced Statistical Inference

Class Information

- Class time: M 1830-2115
- Location: YIA LT7
- Outline: 2025Fall_S5010_outline.pdf
- Password: see Blackboard

Instructor

- Name: Kin Wai CHAN
- Email: kinwaichan@cuhk.edu.hk
- Office: LSB 115
- Tel: 3943 7923
- Office hour:
  I have an open-door policy. Feel free to drop by anytime and ask me questions.

Teaching Assistants

Yi Ho (Henry) NGAN

Email: yihongan@link.cuhk.edu.hk
Office: LSB G30
Tel: 3943 8534

Zhuohua (Joshua) SHEN

Email: zhuohuashen@link.cuhk.edu.hk
Office: LSB G30
Tel: 3943 8534

Description

This course is concerned with the fundamental theory of statistical inference. It covers statistical models, point estimation, set estimation, hypothesis testing, decision theory, large sample theory, methods for evaluating inference procedures, and computational strategies.

Note: Knowledge of Stat 2001, 2006, and 4003 is strongly recommended.

Textbooks

A self-contained lecture note is the main source of reference. Complementary textbooks include

- - (Major) Casella, G. and Berger, R. L. (2002). Statistical Inference. Duxbury Press.
  - (Minor) van der Vaart, A. W. (2000). Asymptotic Statistics. Cambridge.
  - (Minor) Lehmann, E. L. and Casella, G. (1998), Theory of Point Estimation. Springer.
  - (Minor) Lehmann, E. L. and Romano, J. P. (2005), Testing Statistical Hypotheses. Springer.
  - (Minor) Wasserman, L. (2013). All of statistics: a concise course in statistical inference. Springer.

Learning outcomes

Upon finishing the course, students are expected to

understand the foundation of statistical models and statistical inference;
provide intuitive interpretations and statistical insights on various statistical inference problems;
derive and compute statistical inference procedures based on different principles and methods; and
evaluate and compare different statistical inference procedures.

Assessment and Grading

There are three main assessment components, plus a bonus component.

- - a (out of 100) is the average score of approximately eight assignments with the lowest two scores dropped;
  - m (out of 100) is the score of mid-term project/test; and
  - f (out of 100) is the score of final project/exam.
  - b (out of 2) is the bonus points, which will be given to students who actively participate in class.

The total score t (out of 100) is given by

t = min{100, 0.3a + 0.2max(m,f) + 0.5f + b}

If min(t, f ) < 30, the final letter grade will be handled on a case-by-case basis. Otherwise, your letter grade will be in the A range if t ≥ 85, at least in the B range if t ≥ 65, at least in the C range if t ≥ 55.

* For the most updated information, please always refers to the course outline announced by the course instructor in Blackboard, which shall prevail the above information if there is any discrepancy.

Lecture Notes

* Click (S5010/2025Fall/lecture) to download lecture notes.
* The finalized version of the lecture notes will be uploaded one day before the lecture.
* All rights reserved by the authors. Re-distribution by any means is strictly prohibited.

Front Matters

- Contents
- Instructions

Part I: Basic Probability and Statistics

- § 1 Basic Probability: (a) random variables, (b) quantile function, (c) probability inequalities, (d) representation
- § 2 Limit Theorems in Statistics: (a) stochastic convergence, (b) law of large number, (c) central limit theorem, (d) Delta method

Part II: Data Reduction

- § 3 Statistical Models: (a) exponential family, (b) location-scale family, (c) identifiable family.
- § 4 Sufficiency Principle: (a) minimal sufficiency, (b) factorization theorem, (c) ancillary, (e) completeness.
- § 5 Likelihood Principle: (a) likelihood function, (b) discussion

Part III: Point Estimation

- § 6 Qualities of Point Estimators: (a) mean squared error, (b) consistency, (c) efficiency, (d) Fisher information, (e) Cramer-Rao lower bound
- § 7 Methods of Point Estimation: (a) method of moment, (b) unbiasedness, (c) maximum likelihood

Part IV: Hypothesis Testing

- § 8 Qualities of Hypothesis Tests: (a) size and level, (b) power (c) p-value
- § 9 Methods of Hypothesis Tests: (a) most powerful test, (b) likelihood ratio test, (c) Wald test, (d) Rao score test

Part V: Interval Estimation

- § 10 Qualities of Interval Estimators: (a) coverage probability, (b) expected width
- § 11 Methods of Interval Estimation: (a) Pivotal quantity, (b) inversion of tests, (c) bootstrapping

Appendixes

- § A: Basic Mathematics: (a) mathematics notations, (b) differentiation, (c) integration, (d) Taylor’s Expansion
- § B: Solution to end-of-chapter examples (It may contain errors. Please read with care.)
- P.S.: Not all materials in the appendices are directly useful for this course. I will tell you which parts are useful when we need them.

Assignments

* Click (S5010/2025Fall/A) to download assignments.
* Please submit your assignment to the department's dropbox (next to LSB 123). For your convenience, our TAs will collect assignments in class from 18:30 to 18:45 every Monday. Email submissions will NOT be accepted.

- Assignment 1: Basic probability, convergence concepts, limit theorems in Statistics --- Due: 26 Sep (Fri) @1800
- Assignment 2: Exponential family, location-scale family, identifiable family --- Due: 3 Oct (Fri) @1800

In-class notes

* Click (S5010/2025Fall/inclassNote) and (S5010/2025Fall/recording) to download in-class notes and recordings (if any).
* In-class notes and recordings (if any) will be uploaded within one week after the lecture

- Lecture 1 (1 Sep) --- Review, modes of convergence (d, pr, Lp, and a.s.), limit theorems (LLN, CLT, Delta method, CMT, Slutsky theorem), o-notation.
- Lecture 2 (8 Sep) --- Examples of using limit theorems (Eg 2.19, 2.20, 2.21, 2.25, 2.26), proofs of limit theorems (Thm 2.1 [1,2,3,4], Eg 2.4, 2.6, Thm 2.9)
- Lecture 3 (15 Sep) --- Exponential family (NEF, natural parameter space, full rank), location-scale family (representation), identifiable family (missing data)
- Lecture 4 (23 Sep) --- Statistic, SS, MSS, AS, CS

Quizzes

* Click (S5010/2025Fall/quiz) to download quizzes.

- Quiz 1: TBA

Mid-term exam

Start time: 20 October (Monday) @ 6:30 pm
Duration: TBA
Scope: TBA
Instructions: TBA
Mock exam: TBA

Final exam

Start time: 1 December (Monday) @ 6:30 pm
Duration: TBA
Scope: TBA
Instructions: TBA
Mock exam: TBA
Seating plan: TBA

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