This chapter surveys regression techniques that relax functional-form assumptions. Beginning with kernel and local polynomial estimators, we derive bias-variance trade-offs and bandwidth selection criteria. We then explore splines, generalized additive models, regression trees, random forests, and wavelet regression, emphasizing their interpretability and robustness. Multivariate nonparametrics are introduced through radial-basis functions. Confidence-interval construction via asymptotics and bootstrap methods is detailed, and a forward-looking conclusion discusses how nonparametric ideas underpin modern machine-learning algorithms, reinforcing the evolving landscape of regression analysis.

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  • Mike Nguyen

摘要

This chapter surveys regression techniques that relax functional-form assumptions. Beginning with kernel and local polynomial estimators, we derive bias-variance trade-offs and bandwidth selection criteria. We then explore splines, generalized additive models, regression trees, random forests, and wavelet regression, emphasizing their interpretability and robustness. Multivariate nonparametrics are introduced through radial-basis functions. Confidence-interval construction via asymptotics and bootstrap methods is detailed, and a forward-looking conclusion discusses how nonparametric ideas underpin modern machine-learning algorithms, reinforcing the evolving landscape of regression analysis.