Regression splines (parametric Smoothing splines (nonparametric Splines o The preceding is an example of a spline:a piecewise m-1 degree polynomial that is continuous up to its first m-2 derivatives o By requiring continuous derivatives,we ensure that the resulting function is as smooth as possible o We can obtain more flexible curves by increasing the degree of the spline and/or by adding knots o However,there is a tradeoff: Few knots/low degree:Resulting class of functions may be too restrictive(bias) Many knots/high degree:We run the risk of overfitting (variance) Patrick Breheny STA 621:Nonparametric StatisticsIntroduction Regression splines (parametric) Smoothing splines (nonparametric) Splines The preceding is an example of a spline: a piecewise m − 1 degree polynomial that is continuous up to its first m − 2 derivatives By requiring continuous derivatives, we ensure that the resulting function is as smooth as possible We can obtain more flexible curves by increasing the degree of the spline and/or by adding knots However, there is a tradeoff: Few knots/low degree: Resulting class of functions may be too restrictive (bias) Many knots/high degree: We run the risk of overfitting (variance) Patrick Breheny STA 621: Nonparametric Statistics