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課程概述 |
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)
Topics include: VC theory, convergence, point and interval estimation, hypothesis testing and p-values, data reduction, Bayesian inference, and nonparametric statistics. |
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課程目標 |
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. |