Class time: W 0930-1215
Location: YC Liang Hall 104
Outline: 2026Fall_S3005_outline.pdf
Password: see Blackboard
Name: Kin Wai CHAN
Email: kinwaichan@cuhk.edu.hk
Office: LSB 115
Tel: 3943 7923
Office hour: open door policy
Baohao WEI
Email: baohaowei@link.cuhk.edu.hk
Office: LSB G30
Tel: 3943 8534
Junwei (Zero) YU
Email: junweiyu@link.cuhk.edu.hk
Office: LSB G30
Tel: 3943 8534
This course introduces a wide variety of nonparametric techniques for performing statistical inference and prediction, emphasizing both conceptual foundations and practical implementation. Basic theoretical justification is also provided. The content covers three broad themes: (i) rank-type and order-type methods for handling location, dispersion, correlation, distribution and regression problems, (ii) resampling-type procedures for testing and assessing precision, and (iii) smoothing-type techniques for estimation and prediction. Topics include Wilcoxon signed-rank test, Mann-Whitney rank sum test, Spearman’s rho, Kendall’s tau, Kruskal-Wallis test, Kolmogorov-Smirnov test, bootstrapping, Jackknife, subsampling, permutation tests, kernel method, k-nearest neighbour, tree-based method, classification, etc.
Note: No prerequisite but knowledge of Stat 2001, 2005 and 2006 is strongly recommended.
A self-contained lecture note is the main source of reference. Complementary textbooks include
(Major) Bonnini, S., Corain, L., Marozzi, M., and Salmaso, L. (2014). Nonparametric hypothesis testing: rank and permutation methods with applications in R. Wiley.
(Major) Wasserman, L. (2006). All of nonparametric statistics. Springer.
(Minor) Wasserman, L. (2004). All of Statistics: A Concise Course in Statistical Inference. Springer.
(Minor) James, G., Witten, D., Hastie, T., and Tibshirani, R (2013). An Introduction to Statistical Learning: with Applications in R. Springer.
Upon finishing the course, students are expected to
appreciate the beauty of nonparametric methods;
apply a wide variety of nonparametric techniques to perform inference, prediction and learning tasks;
understand the pros and cons of parametric and nonparametric methods;
master the skills in deriving basic theoretical properties of nonparametric methods;
use computer programs to perform nonparametric statistical analysis for real-life problems.
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 a mid-term exam (both written part and coding part); and
f (out of 100) is the score of a final exam (both written part and coding part);
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, 0.2a + 0.3max(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 up-to-date information, please always refer to the course outline announced by the course instructor in Blackboard, which shall prevail over the above information if there is any discrepancy.
Introduction: history, philosophy, examples.
Statistical foundation: basic testing and estimation, statistical limiting theorems.
Location and scale problems: sign test, signed-rank test, rank sum test, Ansari–Bradley test.
Correlation problem: Spearman’s ρ, Kendall’s τ, Bergsma–Dassios’s correlation, Chatterjee correlation
Distribution problem: Kolmogorov–Smirnov test, Cram ́er–von Mises test, Anderson-Darling test.
Permutation tests: ideas of randomization, examples of permutation tests.
Bootstrap and Subsampling: different bootstrapping methods, Jackknife, Subsampling.
Density estimation: histogram, kernel method, bandwidth selection.
Nonparametric regression: Nadaraya–Watson kernel estimator, local polynomial estimator.
Other topics: (a) classification, (b) Bayesian nonparametric, (c) rank-type regression, (d) k-nearest neighbor, ...
* Click (S3005/lecture) to download lecture notes (or click the individual links below).
* The finalized version of the 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
Part I: Philosophy and Foundation
Part II: Rank-type and order-type methods
Chapter 3: Location and scale problems
Chapter 4: Correlation problem
Chapter 5: Distribution problem
Part III: Resampling-type procedures
Part IV: Smoothing-type estimation and learning techniques
Appendices
Appendix A: Basic Mathematics
Appendix B: Basic probability
Appendix C: Basic Statistics
Appendix D: Basic programming in R --- for students who want to review; read Lectures 2 and 3 in RMSC 1101
Appendix E: R-codes used throughout the courses can be found in the lecture folder (this folder will be updated from time to time).
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 (S3005/A) to download assignments.
Assignment 1: concepts of nonparametric methods, theory of ranks, simulation in R --- Due: 2 Oct (Fri) @1800
Assignment 2: rank-type tests, exact and asymptotic critical values, real-data application of urination --- Due: 9 Oct (Fri) @1800
Assignment 3: correlation test, concept of strong correlation, computation formula, real-data application of volatility clustering --- Due: 22 Oct (Thu) @1200
In line 74 of the R code: change cor.test0(...)$p.value to cor.test0(...)
* Click S3005/inclassNote to download in-class notes.
* Click here to download last year's lecture recordings for your reference.
* In-class notes will be uploaded within one week after the lecture.
Lecture 1 (9 Sep) --- Rank, sign, order statistics, order; CIID, CIM, CIIDS, IID; theory
Lecture 2 (16 Sep) --- Five rank-type tests, simulation of power
On page 5, the signed rank test statistic is T = 1/(n+1) \sum_{i=1}^n \psi_i R_i^+, where 1/(n+1) was missing in the original version.
Lecture 3 (23 Sep) --- Theory of rank-type test, examples, exact p-value, tie-adjustment
Lecture 4 (30 Sep) --- Real-data analysis, inference based on signed rank test, weak/strong correlation
Lecture 5 (7 Oct) --- Spearman, Kandall, Bergsma–Dassios correlation
Lecture 6 (14 Oct) --- Chatterjee correlation, coding exercise (finite-sample critical value, power)
Chatterjee correlation original article: https://arxiv.org/abs/1909.10140
Lecture 7 (21 Oct) --- qq-plot, Pearson's chi-squared test, G-test, KS test, CvM test, AD test
Start time: 23 Oct (Fri) @ 6:30 pm (Please arrive 15 minutes earlier.)
Duration: 2 hours
Location: LSB G25, 125 (Seat plan: 2026Fall_S3005_M_seatPlan.pdf)
Scope: Chapters 1-4
Instructions: TBA
Mock papers:
S3005/2025Fall/M *** Most relevant ***
Start time: xxx (xxx) @ xxx pm
Duration: TBA
Location: TBA
Scope: TBA
Instructions: See the Blackboard announcement.
Seat plan: TBA
Mock papers: