課程資訊

Statistics

108-2

MATH3601

201 38100

3.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1082MATH3601_

Contents:
1. Probability language: Description of random phenomenon, sampling variation,
assessment by simulation, sample mean and variance etc. (Rice Chapters 1, 2, and 3;
Wasserman Chapters 1, 2, and 3)
2. Type of Convergence. Law of Large Numbers, Central limit theorem and Delta Method (Rice
Chapters 4 and 5), Simulation (part of Chapters 8 and 24; Wasserman Chapters 4 and 5,
Ch 8.1 and 11.4)
3. Models (Parametric and nonparametric), Fundamental Concepts in Inference including
point estimation, confidence sets, and Hypothesis Testing (Chapter 6)
4. Empirical distribution function (Chapter 7)
5. Resampling: Bootstrap and Jackknife (Wasserman: Chapter 8)
6. Parametric Inference: Estimation and Assumptions Checking (Wasserman: Chapters 9 and 10)
7. Linear and Logistic Regression (Wasserman: Chapter 13, We may skip this topic.)
Topics include: VC theory, convergence, point and interval estimation, hypothesis testing
and p-values, data reduction, Bayesian inference, and nonparametric statistics.

Teach the fundamentals of theoretical statistics.
Provide excellent preparation for advanced work in statistics and machine learning.
Introduce the role of statistics in contemporary applications and to develop an elementary understanding of, and fluency in, the statistical paradigm of data collection, exploration, modeling and inference. Inference includes estimation, interval estimation and hypothesis testing.
Both small and large sample theorems of hypothesis testing, interval estimation, and confidence intervals will cover.

One year Calculus and 機率導論 or equivalent.
Know the material in Chapters 1-3 of of the book (basic probability).

Office Hours

References:
1. Casella, G. and Berger, R. L. (2002). Statistical Inference. 2nd ed. Duxbury Press. (Textbook for

Wasserman (2004). All of Statistics: A Concise Course in Statistical Inference, Springer.
https://www.ic.unicamp.br/~wainer/cursos/1s2013/ml/livro.pdf