Description Usage Arguments Details Value Note Author(s) References See Also
This function implements a local polinomial estimation for the log spectral density at a point x0
\in R^2.
1 | locmulti(x0, l_period, n, freq, h)
|
x0 |
Point \in R^2 at which the spectral density estimate is evaluated. |
l_period |
Vector of length |
n |
Number of points in the analyzed lattice. |
freq |
|
h |
Kernel bandwidth. |
locmulti
function is auxiliary for the nonparametric estimation of the sources spectral density step of the scICA
function. locmulti
function implements the initial estimates for the local maximum likelihood estimator of the log spectral density m(\code{x0}) at a point x0
\in R^2. To obtain an estimate of m(\code{x0}) the local likelihood function
∑_{k}≤ft(Y_k - a - \textbf{b}'(\boldsymbol{ω}_k - x0) - e^{Y_k - a - \textbf{b}'(\boldsymbol{ω}_k - x0)} \right)K_H(\boldsymbol{ω}_k - x0)
is constructed, where Y_k denotes the log-periodogram value at the Fourier frequency \boldsymbol{ω}_k, K_H a surface kernel and H=(h,h). The local maximum estimator \widehat{m}_{LK}(\code{x0}) is \widehat{a} in the maximizer (\widehat{a},\widehat{\textbf{b}}). The estimate is implemented directly in the scICA
function through a Newton-Rapshon algorithm. The initialization for the Newton-Rapshon algorithm is derived through a local polynomial approximation implemented in this locmulti
function. In particular the following function is minimized to find a local polynomial approximation for m(\code{x0})
∑_{k}≤ft(Y_k - a - \textbf{b}'(\boldsymbol{ω}_k - x0) \right)^{2}K_H(\boldsymbol{ω}_k - x0)
and the minimizer \widehat{a} is used as an initial value in order to obtain the local maximum likelihood estimator \widehat{m}_{LK}(\code{x0}).
It returns a list containing the following component:
ahat |
local polynomial estimate of the log spectral density at |
It is auxiliary for scICA
function.
Lee, S., Shen, H., Truong, Y. and Zanini, P.
Shen, H., Truong, Y., Zanini, P. (2014). Independent Component Analysis for Spatial Processes on a Lattice. MOX report 38/2014, Department of Mathematics, Politecnico di Milano.
Fan, J., Kreutzberger, E. (1998). Automatic Local Smoothing for Spectral Density Estimation. Scandinavian Journal of Statistics, 25, 359–369.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.