fda (version 2.4.0)

smooth.morph: Estimates a Smooth Warping Function

Description

This function is nearly identical to smooth.monotone but is intended to compute a smooth monotone transformation $h(t)$ of argument $t$ such that $h(0) = 0$ and $h(TRUE) = TRUE$, where $t$ is the upper limit of $t$. This function is used primarily to register curves.

Usage

smooth.morph(x, y, WfdPar, wt=rep(1,nobs),
             conv=.0001, iterlim=20, dbglev=0)

Arguments

x

a vector of argument values.

y

a vector of data values. This function can only smooth one set of data at a time.

WfdPar

a functional parameter object that provides an initial value for the coefficients defining function $W(t)$, and a roughness penalty on this function.

wt

a vector of weights to be used in the smoothing.

conv

a convergence criterion.

iterlim

the maximum number of iterations allowed in the minimization of error sum of squares.

dbglev

either 0, 1, or 2. This controls the amount information printed out on each iteration, with 0 implying no output, 1 intermediate output level, and 2 full output. If either level 1 or 2 is specified, it can be helpful to turn off the output b

Value

• A named list of length 4 containing:
• Wfdobj
  a functional data object defining function $W(x)$ that that optimizes the fit to the data of the monotone function that it defines.
• Flist
  a named list containing three results for the final converged solution: (1) f: the optimal function value being minimized, (2) grad: the gradient vector at the optimal solution, and (3) norm: the norm of the gradient vector at the optimal solution.
• iternum
  the number of iterations.
• iterhist
  a by 5 matrix containing the iteration history.

See Also

smooth.monotone, landmarkreg, register.fd