STAT444 Lecture Notes - Lecture 10: Cubic Hermite Spline, Dfa Records, Linear Combination
9 Feb 2018
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The solution to fa ( x ) argmfin { [ yi fcxi ) ]2txfi[ f " ( x )]2dx } is a. Ix ) fs ( xtxtxnhxty ( nj ( xil ) Nje = 1% nj and ( ) ni ( ) dx of: f. ( pdf. Ha y, dfa = trace ( ha ) smoothing spline. Remarks: when n x_i values are distinct, the model seems to be over- parameterized as we t n data points with a model with n parameters. Unlike in cubic spline or ncs where the # of knots controls the smoothness, the roughness pending controls the smoothness in smoothing spline: it is common to denote as to represent the sommther matrix. A smoothing spline with xed is an example of a linear smoother because each element of. Given knot locations, there are many alternative but equivalent basis for (cubic) spline. One practically useful one is the b-spline, whose basis functions are strictly local.
