課程資訊
課程名稱
 無母數迴歸
Nonparametric Regression 
開課學期
 112-2 
授課對象
 理學院  統計與數據科學研究所  
授課教師
 江其衽 
課號
 STAT5012 
課程識別碼
 250 U0120 
班次
  
學分
 3.0 
全/半年
 半年 
必/選修
 選修 
上課時間
 星期一4(11:20~12:10)星期三7,8(14:20~16:20) 
上課地點
 新201新201 
備註
 限碩士班以上 且 限本系所學生(含輔系、雙修生)
總人數上限：20人 
  
課程簡介影片
 
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課程概述

This course aims to introduce the nonparametric regression techniques, essentially referring to smoothing procedures for curve estimation, that provide a flexible approach to explore the relationship between a response and a few associated covariates without specifying a parametric model. Those commonly employed techniques (such as kernel smoothing methods and basis-based approaches) along with their statistical properties will be introduced. Some related topics such as dimension reduction and functional data analysis will be covered as well. 

課程目標
 Those commonly employed approaches for nonparametric regression will be introduced. After taking the course, students are expected to comprehend the fundamental, utilize the approaches properly and perform sensible data analysis in addition to be familiar with research questions in this domain. 
課程要求
 Calculus, Statistics, and Linear Regression. 
預期每週課後學習時數
  
Office Hours
 另約時間 
指定閱讀
  
參考書目
 1. Hastie, Tibshirani and Friedman (2016). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2nd edition. Springer. https://hastie.su.domains/ElemStatLearn/
2. Scott (2015). Multivariate Density Estimation: Theory, Practice, and Visualization. 2nd Edition. Wiley.
3. Takezawa (2005). Introduction to Nonparametric Regression. Wiley
4. Gyorfi, Kohler, Krzy?ak and Walk (2002). A Distribution-Free Theory of Nonparametric Regression. Springer.
5. Tsybakov (2009). Introduction to Nonparametric Estimation. Springer.
6. Wahba (1990) Spline Models for Observational Data (https://epubs.siam.org/doi/book/10.1137/1.9781611970128) 
評量方式
(僅供參考)
    
針對學生困難提供學生調整方式
  
上課形式
作業繳交方式
考試形式
其他
 由師生雙方議定
課程進度
週次
日期
單元主題
第1週
 02/19/2024  Introduction 
第1週
 02/21/2024  Review
Empirical CDF
Kernel Density Estimator 
第2週
 02/26/2024  Kernel Density Estimator: bias and variance 
第3週
 03/04/2024  Kernel Density Estimator: asymptotic normality 
第3週
 03/06/2024  Kernel Density Estimator: MISE, CV, Derivatives, Optimal Kernel, Equivalent Kernels, and Boundary Kernels.  
第4週
 03/11/2024  Kernel Density Estimator: Variable Kernels, Multivariate 
第4週
 03/13/2024  Kernel Density Estimator: Computation and Applications
N-W Kernel Estimator: Asymptotic Normality
Local Polynomial Regression: Introduction 
第5週
 03/18/2024  Local Polynomial Regression: Asymptotics 
第5週
 03/20/2024  Local Polynomial Regression: Asymptotics, CV, GCV, variable bandwidth 
第6週
 03/25/2024  Multivariate Nonparametric Regression:
1. Local Linear (bias) 
第6週
 03/27/2024  Multivariate Nonparametric Regression:
1. Local Linear (bias, variance, boundary points)
2. Local Quadratic (bias, variance, boundary points) 
第7週
 04/01/2024  Multivariate Nonparametric Regression:
1. Higher-degree polynomials (p=1, bias, variance, boundary points)
2. Devriatives 
第7週
 04/03/2024  Semiparametric Regression:
1. Introduction
2. SLS, WSLS
3. ADE 
第8週
 04/08/2024  Semiparametric Regression:
4. Density Weighted ADE 
第8週
 04/10/2024  Semiparametric Regression:
5. Sliced Inverse Regression
6. MAVE 
第9週
 04/15/2024  Semiparametric Regression:
6. MAVE 
第9週
 04/17/2024  Midterm Exam 
第10週
 04/22/2024  Semiparametric Regression:
6. MAVE 
第10週
 04/24/2024  Semiparametric Regression:
7. Partial Linear Model
8. Projection Pursuit Regression
Functional Data Analysis
1. Introduction 
第11週
 04/29/2024  Functional Data Analysis
2. Functional Principal Component Analysis