powerpen | Language Reference for FDA Library
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powerpen(basisobj, Lfdobj=int2Lfd(2))
Lfdobj
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A roughness penalty for a function x(t) is defined by integrating the square of either the derivative of x(t) or, more generally, the result of applying a linear differential operator L to it. The most common roughness penalty is the integral of the square of the second derivative, and this is the default. To apply this roughness penalty, the matrix of inner products produced by this function is necessary.
# set up an power basis with 3 basis functions. # the powers are 0, 1, and 2. basisobj <- create.power.basis(c(0,1),3,c(0,1,2)) # compute the 3 by 3 matrix of inner products of second derivatives penmat <- powerpen(basisobj)