在文獻上，對於配適加法模型建立在局部線性迴歸模型中，平滑倒退擬合方法已經被證明它有比古典倒退擬合方法較好的理論性質，然而，平滑倒退擬合方法的演算法較複雜以致於較難應用，而在我們的研究中，我們希望可以建立一個關於古典與平滑倒退擬合方法的連結，並證明平滑倒退擬合方法它可以被改寫為古典退擬合方法藉由使用在 Huang and Chen (2008) 中所提出的平滑矩陣，而這個連結將使得平滑倒退擬合方法的演算法較容易執行且應用。

Smooth backfitting is shown to have better theoretical properties than classical backfitting for fitting additive models based on local linear regression. However the smooth backfitting algorithm is more complex, leading to limited applications. In our study we establish connections between classical and smooth backfitting and show that the smooth backfitting procedure can be written as a classical backfitting procedure with the smoother matrix in Huang and Chen (2008). The connections allow the smooth backfitting algorithm to be implemented in a much simplified way, making it easier for applications.

1 Introduction 1
2 Background 3
2.1 Additive models 3
2.1.1 Normal equations 3
2.1.2 Backtting algorithm 5
2.1.3 Modied backtting algorithm 6
2.1.4 Explicit solutions 8
2.1.5 Standard errors and degrees of freedom 9
2.1.6 A Bayesian view 9
2.2 Smooth backtting estimator 11
2.2.1 Locol constant smooth backtting estimator 12
2.2.2 Local linear smoother backtting estimator 13
2.3 Local polynomial regression in a projection framework 15
2.3.1 Local polynomial regression 15
2.3.2 Geometric properties of the asymptotic projection matrix 17
3 Additive models based on local polynomial projection 18
4 Connections between classical and smooth backtting 23
5 Simulation study 34
6 Discussion 40
Appendix 42
Tables 42
Figures 48
References 59

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