fitLS {orthogonalsplinebasis}

Fitting splines with penalized least squares.

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

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

Arguments

object

The SplineBasis object to 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,\ldots,k_m). The likelihood is defined by

\sum\limits_{i=1}^n(y_i-b(x_i)\mu) + \int\limits_{k_0}^{k_m} \mu^Tb^{\prime\prime}(t)^Tb^{\prime\prime}(t)\mu dt

The function estimates \mu.

Value

a vector of the control points.

See Also

SplineBasis

Examples

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)