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note19 - Chapter 10 Smoothing Methods 1 Nonparametric...

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Chapter 10. Smoothing Methods 1. Nonparametric Models Statistical Regression y = f ( x ) + ǫ where ǫ ’s are zero mean, uncorrelated, random variables with a common variance σ 2 parametric models * assume that f is known with finitely many unknown parameters β = ( β 1 , . . . , β p ) * depend on the parameters in a linear and/or nonlinear fashion * model inference about f = inference about β nonparametric models * NOT assume any specific form of f * infinite parameters * more replying on the neighbors * outliers and influential points do not affect the results * TOTALLY DEPENDS ON DATA additive model f ( x ) = f 1 ( x 1 ) + f 2 ( x 2 ) + · · · + f d ( x d ) * assuming additivity of effects * no interaction * no assumption for each functions * compromise between linear models and nonparametric models * discover the appropriate shape of each of the covariate effects 1
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Nonparametric Models Example: simulated data set from y = f ( x ) + ǫ where x = (1 : 100) / 100 f ( x ) = 1 3 braceleftBig exp parenleftBig x 3 parenrightBig - 2 exp ( - 7 x ) + sin(9 x ) + 1 bracerightBig
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