課程資訊
課程名稱
 無母數迴歸
Nonparametric Regression 
開課學期
 111-2 
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
 星期一3(10:20~11:10)星期三7,8(14:20~16:20) 
上課地點
 新301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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課程大綱
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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. Györfi, Kohler, Krzyżak 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
 2/20/2023  Introduction 
第1週
 2/22/2023  Review
Empirical CDF
Kernel Density Estimator 
第2週
 03/01/2023  Bias and Variance of KDE
Asymptotic Normality of KDE 
第3週
 03/06/2023  MISE ofKDE
Oracle Bandwidth 
第3週
 03/08/2023  KDE: Estimation of Derivatives
Choice of Kernel
Adaptive Smoothing 
第4週
 03/13/2023  KDE: Multivariate (product kernel, general multivariate kernel)
Aspects of Computation 
第4週
 03/15/2023  Aspects of Computation
KDE Application
NW Estimator: Asymptotical Normality 
第5週
 03/20/2023  NW Estimator: Asymptotical Normality 
第5週
 03/22/2023  Local Linear Estimator: Asymptotical Normality 
第6週
 03/27/2023  Local Linear Estimator: Asymptotical Normality 
第6週
 03/29/2023  Local Linear Estimator: Asymptotical Normality
Bandwidth Selection: CV, GCV 
第7週
   Holidays 
第8週
 04/10/2023  Local Linear Estimator: Variable Bandwidth 
第8週
 04/12/2023  Midterm Exam 
第9週
 04/17/2023  Local Linear Estimator: multivariate 
第9週
 04/19/2023  Local Linear Estimator: multivariate 
第10週
 04/24/2023  Local Linear Estimator: multivariate, boundary points 
第10週
 04/26/2023  Local Polynomial Estimator: multivariate, derivatives
Seminparametric Regression: introduction, single index model 
第11週
 05/01/2023  Seminparametric Regression: single index model, ADE 
第11週
 05/03/2023  Semiparametric Regression: ADE, Weighted ADE, Inverse Regression 
第12週
 05/08/2023  Semiparametric Regression: SIR, MAVE
 
第12週
 05/10/2023  Semiparametric Regression: MAVE, Partial Linear Models, Projection Pursuit Regression 
第13週
 05/15/2023  Basis Expansions and Regularization: piecewise polynomials, cubic spline, natural cubic spline 
第13週
 05/17/2023  Basis Expansions and Regularization: natural cubic splines, b-splines, smoothing splines, multidimensional splines. 
第14週
 05/22/2023  Basis Expansions and Regularization: RKHS 
第14週
 05/24/2023  Basis Expansions and Regularization: RKHS, wavelet 
第15週
   Final Project Presentations 
第16週
   Final Project Presentations