fda (version 6.1.8)

int2Lfd: Convert Integer to Linear Differential Operator

Description

This function turns an integer specifying an order of a derivative into the equivalent linear differential operator object. It is also useful for checking that an object is of the "Lfd" class.

Usage

int2Lfd(m=0)

Value

a linear differential operator object of the "Lfd" class that is equivalent to the integer argument.

Arguments

m

either a nonnegative integer or a linear differential operator object.

Details

Smoothing is achieved by penalizing the integral of the square of the derivative of order m over rangeval:

m = 0 penalizes the squared difference from 0 of the function

1 = penalize the square of the slope or velocity

2 = penalize the squared acceleration

3 = penalize the squared rate of change of acceleration

4 = penalize the squared curvature of acceleration?

References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

Examples

# Lfd to penalize the squared acceleration
# typical for smoothing a cubic spline (order 4)
int2Lfd(2)

# Lfd to penalize the curvature of acceleration
# used with splines of order 6
# when it is desired to study velocity and acceleration
int2Lfd(4)