File:06-smooth-means-roughness-penalty.png

Figure file · Smooth means

The roughness penalty \lambda\int\{g''(x)\}^2\,\mathrm{d}x at work. As \lambda\to0 the penalised fit becomes the interpolating cubic spline; as \lambda\to\infty it becomes the least-squares straight line; an intermediate \lambda follows the trend and ignores the noise.

The roughness penalty \lambda\int\{g''(x)\}^2\,\mathrm{d}x at work. As \lambda\to0 the penalised fit becomes the interpolating cubic spline; as \lambda\to\infty it becomes the least-squares straight line; an intermediate \lambda follows the trend and ignores the noise.

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Summary

Description. The roughness penalty \lambda\int\{g''(x)\}^2\,\mathrm{d}x at work. As \lambda\to0 the penalised fit becomes the interpolating cubic spline; as \lambda\to\infty it becomes the least-squares straight line; an intermediate \lambda follows the trend and ignores the noise.

Appears in. Smooth means

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