est.sigma2 {dSTEM}

Estimate variance of smoothed Gaussian noise

Description

Estimate variance of smoothed Gaussian noise through its second-order derivative

Usage

est.sigma2(x, gamma, k = 0.5)

Arguments

x

numerical vector of second-order derivative of kernel smoothed data

gamma

bandwidth of Gaussian kernel

k

numerical value, local maxima (minima) are presumed beyond Mean(x) ± k*SD(x)

Value

value of estimated variance of smoothed noise

Examples

l=15000; h = seq(150,l,150)
jump = rep(0,length(h)+1); b1 = seq(from=0,by=0.15,length = length(h)+1)
signal = gen.signal(l,h,jump,b1)
data = signal + rnorm(length(signal),0,1) # standard white noise
gamma = 10
ddy = diff(smth.gau(data,gamma),differences=2)
est.sigma2(ddy,gamma,k=0.5) # true value is \eqn{\frac{1}{2\sqrt{pi}\gamma}}