Fitting splines with penalized least squares.

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Description

Estimates the control vector for a spline fit by penalized least squares. The penalty being the penalty parameter times the functional inner product of the second derivative of the spline curve.

Usage

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fitLS(object, x, y, penalty = 0)

Arguments

object

The SplineBasis object ot be used to make the fit

x

predictor variable.

y

response variable.

penalty

The penalty multiplier.

Details

For numeric vector y, and x, and a set of basis functions, represented in object, defined on the knots (k_0,…,k_m). The likelihood is defined by

sum_i (y_i-b(x_i)mu) + integral mu^T b''(t)^T b''(t) mu dt

The fucntion estimates μ.

Value

a vector of the control points.

Author(s)

Andrew Redd <aredd at stat.tamu.edu>

See Also

SplineBasis

Examples

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knots<-c(0,0,0,0:5,5,5,5)
base<-SplineBasis(knots)
x<-seq(0,5,by=.5)
y<-exp(x)+rnorm(length(x),sd=5)
fitLS(base,x,y)