Forward Haar-Fisz transform for binomial random variables.
Usage
binhf.wd(x, binsize = 1,print.info=FALSE)
Arguments
x
data vector of binomial observations, of length a power of two.
binsize
the binomial size corresponding to x.
print.info
boolean to print some information about the coefficients.
Value
l
a list of two components transformed: transformed observations corresponding to x and cnew:
scaling coefficient vector used in Fisz modification. This needs to be passed on to invbinhf.wd.
Details
The procedure performs the Haar wavelet transform on the data x, and then modifies the wavelet coefficients by \(f_jk=d_jk/\sqrt{c_jk*(N-c_jk)/2N}\). The inverse Haar transform is then performed. This modification will stabilize the variance of the resulting vector.
References
Nunes, M.A. and Nason, G.P. (2009) A Multiscale Variance Stabilization for binomial sequence proportion estimation, Statistica Sinica,
19(4), 1491-1510.