Class time: M 1830-2115
Location: YIA LT7
Outline: 2025Fall_S5010_outline.pdf
Password: see Blackboard
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.
Email: yihongan@link.cuhk.edu.hk
Office: LSB G30
Tel: 3943 8534
Email: zhuohuashen@link.cuhk.edu.hk
Office: LSB G30
Tel: 3943 8534
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.
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.
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.
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.
* 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.
Contents
Instructions
§ 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
§ 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
§ 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
§ 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
§ 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
§ 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.
* Click (S5010/2025Fall/A) to download assignments.
Assignment 1: Basic probability, convergence concepts, limit theorems in Statistics --- Due: 26 Sep (Fri) @1800
* 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.
Start time: 20 October (Monday) @ 6:30 pm
Duration: TBA
Scope: TBA
Instructions: TBA
Mock exam: TBA
Start time: 1 December (Monday) @ 6:30 pm
Duration: TBA
Scope: TBA
Instructions: TBA
Mock exam: TBA
Seating plan: TBA