These functions fit freeknot splines to data with one independent variable and one dependent variable. It is assumed that the number of knots is known in advance. freelsgen
and freelsgold
fit leastsquares splines with no penalty, while freepsgen
and freepsgold
fit penalized splines. freelsgen
and freepsgen
use a genetic algorithm, while freelsgold
and freepsgold
use a blind search augmented with a golden section algorithm.
1 2 3 4  freelsgen(x, y, degree, numknot, seed = 5, stream = 0)
freelsgold(x, y, degree, numknot, seed = 5, stream = 0)
freepsgen(x, y, degree, numknot, seed = 5, stream = 0)
freepsgold(x, y, degree, numknot, seed = 5, stream = 0)

x 
A vector containing the values of the independent variable. 
y 
A vector containing the values of the dependent variable. 
degree 
The degree of the spline fit. 
numknot 
The number of knots. 
seed 
The value of the initial seed. Defaults to 5. 
stream 
The value of the initial stream to be used for parallel programming. Defaults to 0. 
An object of class "freekt
" containing the following components:
x 
A vector containing the x values. 
y 
A vector containing the y values. 
degree 
The degree of the spline fit. 
seed 
The value of the initial seed. 
stream 
The value of the stream. 
lambda 
The optimum amount of penalty. This is automatically equal to 0 for 
optknot 
A vector containing the optimal knots. 
tracehat 
The trace of the hat matrix for the optimal fit. 
GCV 
The value of generalized cross validation (GCV) for the optimal fit. 
GSJS 
The GSJS estimator, an estimator of the variance of the data. 
call 
The function call. 
Steven Spiriti, Philip Smith, and Pierre Lecuyer
Eubank, R. (1999), Nonparametric Regression and Spline Smoothing, New York: Marcel Dekker, Inc., Second ed.
Spiriti, S., Eubank, R., Smith, P., Young, D., "Knot Selection for LeastSquares and Penalized Splines," Journal of Statistical Computation and Simulation, in press.
fit.search.numknots
for the case where the number of knots is not specified in advance.
1 2 3 4 5 6 
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