smashr (version 1.3-12)

ti.thresh: TI thresholding with heteroskedastic errors.

Description

TI thresholding with heteroskedastic errors.

Usage

ti.thresh(
  x,
  sigma = NULL,
  method = "smash",
  filter.number = 1,
  family = "DaubExPhase",
  min.level = 3,
  ashparam = list()
)

Value

returns a vector of mean estimates

Arguments

x

The data. Should be a vector of length a power of 2.

sigma

The standard deviation function. Can be provided if known or estimated beforehand.

method

The method to estimate the variance function. Can be 'rmad' for running MAD as described in Gao (1997), or 'smash'.

filter.number

The wavelet basis to be used.

family

The wavelet basis to be used.

min.level

The primary resolution level.

ashparam

Passed as the “ashparam” argument in the call to smash.gaus.

Details

The 'rmad' option effectively implements the procedure described in Gao (1997), while the 'smash' option first estimates the variance function using package smash and then performs thresholding given this variance function.

References

Gao, Hong-Ye (1997) Wavelet shrinkage estimates for heteroscedastic regression models. MathSoft, Inc.

Examples

n=2^10
t=1:n/n
spike.f = function(x) (0.75*exp(-500*(x-0.23)^2) +
  1.5*exp(-2000*(x-0.33)^2) +
  3*exp(-8000*(x-0.47)^2) +
  2.25*exp(-16000*(x-0.69)^2) +
  0.5*exp(-32000*(x-0.83)^2))
mu.s = spike.f(t)

# Gaussian case
# -------------
mu.t=(1+mu.s)/5
plot(mu.t,type='l')
var.fn = (0.0001+4*(exp(-550*(t-0.2)^2) +
  exp(-200*(t-0.5)^2) + exp(-950*(t-0.8)^2)))/1.35
plot(var.fn,type='l')
rsnr=sqrt(5)
sigma.t=sqrt(var.fn)/mean(sqrt(var.fn))*sd(mu.t)/rsnr^2
X.s=rnorm(n,mu.t,sigma.t)
mu.est.rmad<-ti.thresh(X.s,method='rmad')
mu.est.smash<-ti.thresh(X.s,method='smash')
plot(mu.t,type='l')
lines(mu.est.rmad,col=2)
lines(mu.est.smash,col=4)