Smoothing Splines

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• Smoothing Splines
• Penalized Splines

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1. Smoothing Splines
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Roughness of a function
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Limit the Roughness
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Smoothing Spline Criterion
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General Order Smoothing Spline
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Cubic Smoothing Spline
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Cubic Smoothing Spline
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The Cubic Smoothing Spline Smoother
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Choice of the smoothing parameter
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2. Penalized Splines
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Drawbacks of the Existing Spline Methods
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Key Idea
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Penalized Spline Criterion
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The P-Spline Smoother
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Choice of the smoothing parameter