fit.search.numknots: Perform a Search on the Number of Knots and Fit Free-Knot...

In freeknotsplines: Algorithms for Implementing Free-Knot Splines

Description

This function fits free-knot splines to data using every value for the number of knots between minknot and maxknot. The number of knots is then chosen to optimize a fit criterion. The free-knot spline with the optimum number of knots is returned.

Usage

fit.search.numknots(x, y, degree, minknot = 1, maxknot = 5, 
                   alg = "LS", search = "genetic",
                   knotnumcrit = "adjGCV", k = 2, d = 3, seed = 5,
                   stream = 0)

Arguments

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.
minknot	The minimum number of knots to search. Defaults to 1.
maxknot	The maximum number of knots to search. Defaults to 5.
alg	The spline-fitting algorithm. Choices are "LS" for least-squares and "PS" for P-splines. Defaults to "LS."
search	The random search algorithm. Choices are "genetic" for a genetic algorithm and "golden" for a blind random search with golden section adjustment. Defaults to "genetic."
knotnumcrit	The criterion to be used for determining the number of knots. Choices are "GCV" for generalized cross-validation, "AIC" for the Akaike information criterion, "AICc" for corrected Akaike information criterion, "BIC" for Bayesian information criterion, "adjAIC" for an adjusted version of the Akaiki information criterion, and "adjGCV" for an adjusted version of generalized cross-validation. Defaults to "adjGCV."
k	The amount of penalty when AIC is used. Has no effect with criteria other than AIC. Defaults to 2.
d	The amount of penalty when adjGCV is used. Has no effect with criteria other than adjGCV. Defaults to 3.
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.

Value

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 freelsgen and freelsgold.
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.

Author(s)

Steven Spiriti

References

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 Least-Squares and Penalized Splines," Journal of Statistical Computation and Simulation, in press.

See Also

fitcriteria for the fit criteria, freeknotfit for the free-knot spline algorithms.

Examples

x <- 0:30/30
truey <- x*sin(10*x)
set.seed(10556)
y <- truey + rnorm(31, 0, 0.2)
xy.freekt <- fit.search.numknots(x, y, degree = 2, minknot = 1, maxknot = 3, seed = 555)
plot.freekt(xy.freekt, xfit = 0:1000/1000)

Example output

Loading required package: splines
[1] Number of knots = 1, adjGCV = 0.154495348459508
[1] Number of knots = 2, adjGCV = 0.0421612296639563
[1] Number of knots = 3, adjGCV = 0.0587893119696036

freeknotsplines documentation built on May 2, 2019, 8:51 a.m.