ti.thresh: TI thresholding with heteroskedastic errors.

In zrxing/smash: Smoothing by Adaptive Shrinkage in R

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()
)

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.

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.

Value

returns a vector of mean estimates

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)

zrxing/smash documentation built on July 12, 2024, 6:31 a.m.